for example, -1/5 isnt in the intersection
#help-10
supple pumice
timid silo
it tends to 0
neon eagle
yes it does
timid silo
and you can check by actually proving the set equality
wdym by that?
upbeat plinth
do you know how to prove two sets are equal
timid silo
a subset b and b subset a
upbeat plinth
yeah so you can check your answer by proving set equality
obtuse pebbleBOT
upbeat plinth
no prob
obtuse pebbleBOT
Available help channel!
copper vault
is the convergence of bisection proportional to the number of the bits used for the mantissa?
obtuse pebbleBOT
is the convergence of bisection proportional to the number of the bits used for ...
random depot
No
The convergence depends on the properties of the function being evaluated and the initial interval used for the method
mighty crown
obtuse pebbleBOT
ruby path
Can you figure out the number of roots this curve has?
mighty crown
3
mighty crown
-3, 2/5, 4
mighty crown
-(x+3)(x-2/5)(x-4) = y ?
mighty crown
oh it's 4 right?
ruby path
yes
mighty crown
-(x+3)(x-2/5)(x-4)^2?
ruby path
yup thats it
mighty crown
yup thats it
oh thanks
how come when i graph it on a calcualtor is says the y-intercept is 19.2 though?
do I still need to edit the equation or is the question written wrong
ruby path
,calc 1630.4
warm shaleBOT
Result:
19.2
ohh
ruby path
$-a(x + 3)(x -\frac25)(x - 4)^2 = y$
warm shaleBOT
NEONPerseus
ruby path
Put (0, 96) and solve for a
mighty crown
-5(x+3)(x-2/5)(x-4)^2) = y
ruby path
Yeah should be good now
hollow cargo
I have a system with K+1 servers. The K first servers have a random, stricty positive service time. The last server has a service time of 0. Basically, the client is ejected. It is ejected with probability proportional to the number of occupied server. Arrival follow a Poisson process. I want to compute the time average of the number of ejected clients. This is actually easy using little's law, and assuming stationarity and ergodicity. But I have no insurance over these two, ergodicity in particular, except when service time on the K first servers is exponential (because the time continuous process counting the occupied server become an easy to dtudy markovian jump process). Is there any ressources to ensure ergodicity in the general case? Or other interesting special cases?
obtuse pebbleBOT
I have a system with K+1 servers. The K first servers have a random, stricty pos...
@hollow cargo Has your question been resolved?
obtuse pebbleBOT
@hollow cargo Has your question been resolved?
terse crater
Hi. I'm given 4 points (a1, b1), (a2, b2), (a3, b3), (a4, b4). Is there a way to elegantly get the equation of the cubic equation that the points correspond to?
In particular, I'd like to find the time (t) required for the cubic represented by the points above to reach a particular y value.
If I have the equation of the cubic, I can use Newton's method or similar to find the roots.
obtuse pebbleBOT
Hi. I'm given 4 points (a1, b1), (a2, b2), (a3, b3), (a4, b4). Is there a way to...
sage geode
You could solve a system of 4 equations
pa1^3 + qa1^2 + sq1 + r = b1
pa2^3 + qa2^2 + sq2 + r = b2
pa3^3 + qa3^2 + sq3 + r = b3
pa4^3 + qa4^2 + sq4 + r = b4
Not sure if there's a better way
Will be easy if you find inverting a 4x4 matrix easy 
terse crater
Ouch. I have access to dy/dt and d2y/dt2 at those points.
Will that make it easier?
sage geode
dt or dx?
warm canopy
Hi. I'm given 4 points (a1, b1), (a2, b2), (a3, b3), (a4, b4). Is there a way to...
Lagrange interpolation is probably what you want for this
sage geode
Meh I don't think those will help then
sage geode
Lagrange interpolation is probably what you want for this
Oh I forgot that even exists lol
Yeah that works too
terse crater
Lagrange interpolation is probably what you want for this
Ok I didn't know what that was. From the description it looks promising. I'll do research and try to use it.
Thanks both for the help. If I'm stuck later I'll come back and re-ask.
.close
proper ivy
Did i prove this correctly?
obtuse pebbleBOT
Did i prove this correctly?
proper ivy
its just that i am not very good with proof questions
royal basin
this looks like it proves $A \cap (B - C) \subseteq (A \cap B) - (A \cap C)$
warm shaleBOT
Ann
twilit pelican
do you remember how to prove equality of sets
royal basin
it's not that you should fix anything, it's that you aren't done yet
you need to prove the inclusion the other way around too
proper ivy
do you remember how to prove equality of sets
yeah we show they are subsets of each other
twilit pelican
yeah we show they are subsets of each other
what ann said, you need the other direction now
you’ve only shown the first is a subset of the second
proper ivy
oh so i should just start over again but with right side of the equation?
twilit pelican
well keep what you wrote rn lol
proper ivy
and derive the left side?
proper ivy
well keep what you wrote rn lol
yeah
twilit pelican
but yes
proper ivy
okay i see
twilit pelican
most likely gonna be backwards of what you wrote originally
timid silo
How to solve the lower example using the upper equality
obtuse pebbleBOT
How to solve the lower example using the upper equality
timid silo
royal basin
посмотрите внимательно на каждую дробь в сумме по отдельности
и поймите, что эти дроби на самом деле равны $\frac{2n+1}{n^2(n+1)^2}$ для $n=1,2,3,4$
warm shaleBOT
Ann
obtuse pebbleBOT
timid silo
спасибо
royal basin
да не за что
obtuse pebbleBOT
Available help channel!
spare crypt
obtuse pebbleBOT
spare crypt
How to do this induction proof?
spare crypt
What have u tried
I can’t seem to factor out 25
lost tree
U factored wrong it seems
When u factored out the 9
U got -9(something + something), it shud instead be -9(something - something)
lost tree
And why have u written 27 * 2
It shud be a minus there
So then u get a 25 that u can factor out
27 - 2
lost tree
😄
spare crypt
.close
mild flint
Small circle and big circle have same center. AB=10 and is tangent for small circle. Find area of black region
obtuse pebbleBOT
Small circle and big circle have same center. AB=10 and is tangent for small cir...
winter cargo
Small circle and big circle have same center. AB=10 and is tangent for small cir...
hope this helps (:
https://www.youtube.com/watch?v=cOcW9SIvP7w
shy vigil
A circle is a group of points that are at a fixed distance from a fixed point. Clearly there are infinite circles in that image.
winter cargo
thats a nice coincidence
mild flint
hope this helps (:
https://www.youtube.com/watch?v=cOcW9SIvP7w
Much appreciated mate.
.close
polar bramble
how do you solve problems like this
obtuse pebbleBOT
how do you solve problems like this
polar bramble
there is no y intercept
and the slope is 0/undefined since its a vertical and horizontal line
normally i would just change it to point slope form
and from there i can get the y intercept
sage geode
The line B is a vertical line, right?
So line A is supposed to be a horizontal line
Meaning the y value everywhere on it is the same
So the equation of line A is just y = 3.5
sage geode
We're given that the point (-1, 3.5) lines on the line A
And, like I said, every point on the line A has the same y value
Meaning it's 3.5
polar bramble
oh i see it
cobalt valve
obtuse pebbleBOT
cobalt valve
Can someone help me with completing this proof
rigid lintel
your induction hypothesis and induction step are a mess
i think youre overcomplicating it for yourself
assume that the statement holds for some k >= 1 then you need to show that it also holds for k+1
thats all you need to do
so write down p(k)
and try to deduce p(k+1) from that
obtuse pebbleBOT
@cobalt valve Has your question been resolved?
cobalt valve
aight thanks
fathom belfry
obtuse pebbleBOT
fathom belfry
how do i compute
obtuse pebbleBOT
@fathom belfry Has your question been resolved?
edgy cargo
I need help with these 2 questions
obtuse pebbleBOT
I need help with these 2 questions
glad zenith
What have you donc so far ? Did you try to form the equation ?
edgy cargo
What have you donc so far ? Did you try to form the equation ?
idk how
<@&286206848099549185>
.close
wheat trout
obtuse pebbleBOT
wheat trout
how do i do this?
sage geode
What's the relation between logm and logR?
warm canopy
just apply log to the values of m
warm canopy
log base 10
wheat trout
tthx
obtuse pebbleBOT
@wheat trout Has your question been resolved?
silver maple
Hello everyone,can i get some on what to do first in this word problem
obtuse pebbleBOT
Hello everyone,can i get some on what to do first in this word problem
silver maple
ionic geyser
the answer is zero because the metal sheet doesn't have thickness 
but on a serious note, you'd probably want to first convert the dimensions to the same units as the density
the metal sheet is shape 2
obtuse pebbleBOT
@silver maple Has your question been resolved?
forest fjord
obtuse pebbleBOT
forest fjord
Where did I go wrong?
warm canopy
forest fjord
-21?
warm canopy
yes
forest fjord
Hmm
warm canopy
why do you think it would be 21
forest fjord
why do you think it would be 21
Wdym
warm canopy
what is the exact question you have been asked
forest fjord
Solve the equation
warm canopy
send a pic of it
warm canopy
no of the actual question
warm canopy
Supposed to be x /E R
where are you getting this from then?
forest fjord
Calculator and solutions from the book
umbral orbit
i think it would be easier if u did diff of perfect squares on the x^2-9
warm canopy
the equation you posted has no real solutions
forest fjord
Supposed to be x /E R
Thats what I said here
/E is supposed to be 'not part of'
Didnt know how to make the symbol here
warm canopy
okay that just wasnt clear
forest fjord
Ye
warm canopy
so what is your issue?
forest fjord
i think it would be easier if u did diff of perfect squares on the x^2-9
Wdym
warm canopy
do it again, be careful with signs
umbral orbit
a^2-b^2 = (a-b)(a+b)
warm canopy
er the 3x^2 cancel from each side
forest fjord
Oop forgot that ye im just tired lol
warm canopy
but yeah then your signs are fine
forest fjord
I just dont understand where I wemt wrong
Or if I took a the wrong approach from the start
Cus x^3-2x+21=0 is solvable
So
Just did it like my calculator said
And I'm left with
warm shaleBOT
Jekkey
forest fjord
Is there a way to prove it has no answer without using the quadratic formula?
Or should I just use that
high lily
you could start with just the discriminant
to determine whether there are real solution(s)
high lily
$\Delta = b^2 - 4ac = ...$
warm shaleBOT
ℝamonov
high lily
and if that's non-negative you can use that value in the QF
$$x = \frac{-b \pm \sqrt{\Delta}}{2a}$$
warm shaleBOT
ℝamonov
forest fjord
I see
In the exam we have to name like the things we're doing, or atleast has to be clear. Do you think just writing delta=... is enough?
high lily
yes
as long as you give a short explanation /interpretation of the result
i.e. in this case Delta = ... < 0
therefore no real soltions
tame escarp
How can I prove a line perpendicular to a plane at a certain point (that’s part of the line)
obtuse pebbleBOT
How can I prove a line perpendicular to a plane at a certain point (that’s part ...
fickle turret
In what form to you have your plane given?
tame escarp
(ABC)
Wait lemme send you the entire given
Im at the last question
Solved everything else
fickle turret
So you already have the plane equation?
fickle turret
Nice, what is the normal vector of the plane then?
tame escarp
Not sure
But shouldnt it be n (A,B,C)?
Those three points being the ones forming the plane
tropic leaf
The normal vector of plane ax+by+cz+d = 0 is (a,b,c)
tame escarp
Oh
split glade
Can’t youn find direction vector of de and dot product with normal
tame escarp
the normal of the plane then is n(1,-1,0)
split glade
And the answer should equal 0 a.b =|a||b|costheta
fickle turret
So if DE is orthogonal to the plane it needs to be z(1,-1,0)
tame escarp
And how do I find DE
split glade
D -E
tame escarp
Alr thanks
split glade
That gives you direction vector which is all you need
fickle turret
Can’t youn find direction vector of de and dot product with normal
No, the normal vector is orthogonal to the plane. So if DE dot N was 0, DE is orthogonal to the orthogonal vector, which means it is parallel to the plane
split glade
Oh yeah my bad
tame escarp
👀
So it’s just finding the direction vector of DE
And it should be equal to the normal
tame escarp
z is just a constant right?
fickle turret
Yes
polar bramble
can someone help me with this word problem
obtuse pebbleBOT
can someone help me with this word problem
polar bramble
i just can't think of a solution
all i figured out is when Ji-Hun starts, Kana will already have ran 0.28 miles
royal basin
0.28 miles...? sounds like there's some error bars on that one
actually wait im not sure that's even correct
how did you get the distance by which kana leads jihun at 10:00 to be 0.28 mi?
polar bramble
0.28 miles...? sounds like there's some error bars on that one
might be wrong actually
polar bramble
you might have to find the LCM
LCM ?
royal basin
no need to worry about that
would be too early even if relevant
how did you get the distance by which kana leads jihun at 10:00 to be 0.28 mi?
split glade
Can’t you solve algebraicly
polar bramble
since its 7 for every 60 minutes
royal basin
!nosols
obtuse pebbleBOT
As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.
royal basin
@polar bramble by your logic the distance she ran in 1 minute would be 7/1 = 7 miles, clearly absurd
you would want 7*(25/60)
7 miles/hour * (25/60) hours
polar bramble
yeah its aprox 3 miles
polar bramble
35/12
royal basin
no
i'm not asking how fast he is running
i am asking how fast he is catching up to kana
i.e. the rate at which the gap between them closes
royal basin
1 mile per hour.
so
(35/12) miles at 1 mile per hour -- how long will it take for the catch up to happen?
(this is of course not the answer YET, but it's a step towards the answer.)
royal basin
35/12 hours, yes
now
jihun runs at 8 miles per hour
in this time, how far will he have traveled?
royal basin
yes
royal basin
sometimes the lack of clarity in a word problem is partially to blame on the problem, but i think not in this case
polar bramble
this for me , is very easy.
all i have to do is.
5L+11S = 41.60
10L+4S = 40.90
then solve
polar bramble
sometimes the lack of clarity in a word problem is partially to blame on the pro...
maybe its because i have been studying for 8hours
xD
royal basin
maybe its because i have been studying for 8hours
bad bad bad
polar bramble
wdym ?
royal basin
take a break
polar bramble
true
but i feel a sense of urgency since my SAT is 1 month away
maybe i should split it
anyways
thank you
.close
timid silo
Hey
timid silo
How do you do translations
split glade
On a 2d graph?
split glade
Always get in terms if y if you can
timid silo
Wdym?
split glade
If the operation is on the outside of function it effects y and does whatnitnlooks like it does for example f(x) +5 draws f(x) five higher
timid silo
It gives us the points tho
trim portal
Convert this to y=something
timid silo
How would I do that?
trim portal
add 3 to both sides?
split glade
Just like normal the function can be treated as a variable
split glade
That’s times 3
trim portal
and you multiplied the right side by 3
trim portal
I meant do +3 on both sides
split glade
F(x) + 3
trim portal
y=f(x)+3
Do you know what kind of translation is that?
https://www.desmos.com/calculator/qjejzenhcz Try changing values of A, and see how the graph transforms. Red function is the original, blue function is translated
obtuse pebbleBOT
@timid silo Has your question been resolved?
dark tundra
obtuse pebbleBOT
dark tundra
Why is this highlighted step true
How did they just turn the complex number into a 13
trim portal
They evaluated magnitude
trim portal
dark tundra
oh wait the absolute value of i is 1, but then why isnt it 13*17
ohhh
ok got it
thx
silver plover
obtuse pebbleBOT
silver plover
when finding the reduced echelon form
r we able to start off by using the 1 as the pivot?
silver plover
Yes you may change tows
do u always have to start at the top most left digit?
robust sleet
Yes
robust sleet
U could interchange the two rows but if u didn't after dividing first row by 2 u should do R2 - R1, so second rows become 0 9 -5
silver plover
U could interchange the two rows but if u didn't after dividing first row by 2 u...
how do u get 9
5 - 1/2(-4) is 5+2 which is 7
silver plover
cant see the mistake ive made
robust sleet
Lol
silver plover
sry
little tinsel
I will have a math competition tomorrow, any tips?
obtuse pebbleBOT
I will have a math competition tomorrow, any tips?
little tinsel
i will have 5 math problems, and 3 hours to do it
fierce lagoon
Use the help channels properly
little tinsel
.close
dire marten
I’m not sure if I did this right, I’m in grade 9 algebra 1 but my fractions is so bad that I somehow get two fifths over one and a half, I need some help on how to do fractions correctly
obtuse pebbleBOT
I’m not sure if I did this right, I’m in grade 9 algebra 1 but my fractions is s...
fathom flicker
okay so you did the first step properly, but what you ended up with was incorrect
it was a good idea to divide both sides by 5/2
but
dire marten
I’m not very good at division either
warm shaleBOT
AustinU
fathom flicker
what should you do when you are dividing by fractions?
keep the top one the same, flip the bottom one, and multiply
keep - change - flip
so that division there is actually
warm shaleBOT
AustinU
fathom flicker
and then what is 2 * 2? and 3 * 5?
dire marten
4/15
fathom flicker
yes perfect
so instead of getting 2/5 divided by 1 and a half
you get 4/15
and it is still being multiplied by x aswell
so you end up with
,, y>=\frac{4}{15} * x
warm shaleBOT
AustinU
fathom flicker
does that make sense?
fathom flicker
if you mean this symbol
it just means multiplication
you can think of multiplying by x
as multiplying by x/1
if that helps you
dire marten
Are they multiplied and divided straight across or with butterfly?
I meant fractions, I’ve seen some people multiply straight across and some people do it like an X
Either 2•2 and 3•5 or 2•5 and 3•2
fathom flicker
when you are multiplying fractions you multiply the top with the top and the bottom with the bottom
so straight across
hazy yew
I have been struggling on this question. Not sure how I'd answer it
obtuse pebbleBOT
I have been struggling on this question. Not sure how I'd answer it
@hazy yew Has your question been resolved?
timid silo
I have been struggling on this question. Not sure how I'd answer it
N3?
you know the radius is 10cm, and the circumference bit is 30cm
and ur trying to find theta
PI * Diameter * (theta/360) = 30cm
use that to help
obtuse pebbleBOT
@hazy yew Has your question been resolved?
steel goblet
I need help with 46
steel goblet
i was thinking this:
there exists a real number x and a real number y such that x is less than or equal to y. The value would be true, right?
sorry just closed the other channel
wary vigil
bigger than or equal to y
but yes in the real numbers there exists and x and y where x >= y
steel goblet
bigger than or equal to y
i misread the question lol
thank you, i really appreciate it!
.close
obtuse pebbleBOT
steel goblet
.reopen
obtuse pebbleBOT
✅
steel goblet
sorry one more question:
in this case, aren't 49 and 50 almost the same thing?
they're both false, right?
timid silo
they're both false, right?
yes but they arent the same
steel goblet
I know order does matter for existential and universal
so for 49 it means:
for all x there exists y...
and 50 it means there exists a y for all x...
right?
smoky panther
obtuse pebbleBOT
smoky panther
can anyone help me with quesiton 1?
smoky panther
no
smoky panther
f'(x)?
meager hull
Well yes but what will f'(x) be
smoky panther
f'(x) = 2x+1
meager hull
Yeah
Now we need to find the slope of the tangent line. This is basically your derivative evaluated at the point
So plug in ur x value in ur derivative
meager hull
Yeah
Exactly
So that is our slope of the tangent line but there is a formula, do u know the formula?
smoky panther
no idea
meager hull
Okay so it's:
Y - Y1 = mtan(x - x1)
Your mtan is the slope we just found
The letters with 1 are also known as y initial or x initial, your starting values of y or x
We have all the information we need to develop the equation of the tangent line now, just have to plug in all of our info
smoky panther
Okay so it's:
Y - Y1 = mtan(x - x1)
Your mtan is the slope we just found
so do i plug in 2 for all of the y?
and 1 for all of the x?
meager hull
No
You leave the y and x as is
The y1 and x1 are the ones you will plug your point values into
meager hull
They just stay the way they are
Because it'll be line/function so we need x and y there
smoky panther
ok so its Y -2 =mtan (x-1)
meager hull
Almost, we just need to plug in our mtan
Remember, our mtan is the slope we found earlier
smoky panther
3 is m
meager hull
Yeah
smoky panther
is 3 m or is 3 mtan
meager hull
Well ig they are interchangeable here
meager hull
No hold on
M is the slope yes
Mtan is just a more specific way of saying it since m means slope, mtan or m tan means slope of the tangent line
Since later in math there will be slope of other types of lines
meager hull
Yeah
meager hull
y-2=3(x-1)
This is right
meager hull
and the second derivative is 0
Dw about the second derivative
And Photomath doesn't answer the question being asked here
smoky panther
oh
meager hull
Ok so yeah ur done! That's the equation of the tangent line
smoky panther
wait really?
smoky panther
the equation of the tangent line is just y-2 = 3(x-1)? shouldn't i isolate y?
meager hull
It's optional
smoky panther
yea i kinda wanna simplify, tbh
meager hull
Well if u want, u can list both
smoky panther
i think thats what my teacher wants to see
meager hull
Rather safe than sorry, just make sure you simplify properly
meager hull
Yeah
smoky panther
Just with different numbers
can I try it and you check my answer?
meager hull
Sure
smoky panther
meager hull
Sorry the image is blurry. What did u get for the derivative of 1/x + x
smoky panther
1
meager hull
That is not the derivative of 1/x + x
smoky panther
oops
meager hull
Yeah
meager hull
I think they are trying to do the derivative atm
smoky panther
getting help from lili_monarch rn, thanks
here, I fixed it
is this correct? the deriv. of the function is - 1/x^2 + 1
and my final answer for the equation to the tang. is $Y= -x+1+x^3+x^2 / x^2$
warm shaleBOT
vanessa.v
meager hull
is this correct? the deriv. of the function is - 1/x^2 + 1
That's the right derivative
But remember, the derivative straight up won't be your mtan, you have to evaluate it at the point for the slope
So you shouldn't have any variables in your slope
smoky panther
But remember, the derivative straight up won't be your mtan, you have to evaluat...
im not sure how to evaluate it for the slope
meager hull
U plug in x into ur derivative
smoky panther
do i plug in 1 as x
meager hull
if i do this i get 0
Then yeah u will get zero
smoky panther
so then it would be Y - 2 = 0(x-1)
then Y = 0(x-1) + 2
then Y = 2
is that correct?
kind of a weird answer
smoky panther
okay, can you help me with either question 3 or 4?
meager hull
Those I can't
smoky panther
no problem 🙂 you already helped a lot
frosty spoke
for question 3, can't you just find the average rate of change over the interval [0, 4]
and solve for where f' equals that
sounds like I'm repeating the question, but it seems like there's a pretty straightforward path
smoky panther
honestly
i dont even wanna do question 3 rn, can you help me with 4
seems a bit less difficult, not sure
frosty spoke
actually number 4 seems like one of those questions that doesn't have an answer
frosty spoke
what's wrong with what I said
find the average rate of change over the interval
and then find out where f' equals that
smoky panther
im not sure how to do that
frosty spoke
do you know what the average rate of change is
smoky panther
yea but I forgot how to find it
frosty spoke
spend a minute, do a quick Google search for the formula
and paste it here
"average rate of change of a function"
smoky panther
frosty spoke
do you understand what that means
smoky panther
tbh not exactly
frosty spoke
okay do you understand what f(b) means
smoky panther
no
frosty spoke
yeah that's a problem
should've covered this a long time ago
f(b) means the value of the function f at the value b
this formula gives you the average rate of change on the interval [a, b]
frosty spoke
yes
smoky panther
okay so i wrote a(x) = f(0) - f(4) / 4 - 0
smoky panther
should i put f(x)
frosty spoke
anyway, it's just the average value of the function is (f(4) - f(0))(4-0)
writing math is not about writing magic
if you don't know what it means, you probably shouldn't be writing it
that would be like writing a book without knowing what the words mean
just communicate what you're thinking
smoky panther
no im just saying like you said a(x) is a bad notation
i was suggesting i write f(x)
frosty spoke
yeah f(x) is even worse notation
because it's not true
A(x) is bad notation because it doesn't depend on x
f(x) = (f(4)-f(0)/4 is just completely false, if one takes f(x) at its standard meaning
in general, just like you won't write random words in a sentence, writing random symbols in math that you've seen somewhere else
smoky panther
so should I just write $A(x) = (f(4) - f(0))(4-0)$
frosty spoke
is not a good idea
warm shaleBOT
vanessa.v
frosty spoke
just write the average rate of change of f is (f(4)-f(0))/4
you're using symbology you don't really understand and borrowed from somewhere
I think A(x) might be taken to mean the running average, which it is decidedly not
there is nothing wrong in general with using English to describe math
smoky panther
you're using symbology you don't really understand and borrowed from somewhere
okay, i have written this down
^ above msg
frosty spoke
might be a little hard to read, but at least you're not saying wrong stuff
frosty spoke
now can you calculate (f(4) - f(0))/4?
frosty spoke
so you're telling me writing (f(4) - f(0))/4 is the same thing as writing ((4)-(0))/4?
smoky panther
i didn't know. can you please explain what i should do
frosty spoke
no but I'm asking you
math is about reasoning
I want to know your reasoning behind things
you're free to do whatever you want, as long as you have sound reasoning behind it
it's not about what you should or shouldn't do
smoky panther
well at first i was calculating it as if it meant f times 4. then you said it doesnt mean that, so i ignored f
frosty spoke
I'm wondering what type of misconception you have that would suggest that i calculated it and just ignored f this would yield the same thing
okay but why would ignoring f give you the correct answer?
smoky panther
im just not understanding exactly what f represents. that is my problem
frosty spoke
logically, if ignoring f would give you the right answer, then doesn't that mean (f(4) - f(0))/4 is the same thing as writing ((4)-(0))/4?
smoky panther
logically, if ignoring f would give you the right answer, then doesn't that mean...
okay i get you're point, ignoring f would be wrong since these two are not the same
what does f represent
smoky panther
yes, but how would I acknowledge that function in my answer?
while solving this, what do i do with f
frosty spoke
math is not about coming up with an answer that will satisfy a teacher
it's about giving a logical argument to support an answer that actually answers the question
there is no requirement to "acknowledge" anything in an answer
and you shouldn't think of it that way
actually, let's back up a little
do you know what the question is asking?
as in do you understand what the question means?
smoky panther
find the point, on the given function so that the derivative of the function is the same as the rate of change over the interval 0<x<4
so i find the rate of change over that interval
then i find the derivative of the given function
they should be equal
frosty spoke
no
you're asked to find a single point
where the derivative is equal to the average rate of change
does that make sense?
frosty spoke
there is no "derivative of that single point"
the derivative of f, evaluated at the point that you found, should equal the average rate of change
smoky panther
okay
smoky panther
no idea
frosty spoke
yeah okay you have massive conceptual gaps in your understanding
you should probably go back and study the definitions conscientiously instead of memorising solutions to problems
but in short, it is
smoky panther
omg
frosty spoke
do you understand what f(x) = x^2 means?
smoky panther
it is a function.
frosty spoke
okay, and what does writing f(x) = x^2 mean, in your own words?
smoky panther
writing that is the equation of a quadratic function that is incresing.
frosty spoke
that's just a word salad
smoky panther
ok clearly this isnt working
frosty spoke
a function is a machine that takes in a number and spits out another number
what does f(x) = x^2 say about the output when you put the number 29 in it?
frosty spoke
I'm giving you a crash course in the definitions
smoky panther
i get that you're trying to help but I learn a different way than your approach to teaching
frosty spoke
you need to learn the definitions and basics before you try to solve problems
like idk what to tell you
I could just give you what to write to make your teacher happy, but then you're just going to memorise to write that the next time you get the problem
but that's not going to actually do anything
smoky panther
I have answered multiple questions already with the help of other people on this server
frosty spoke
yeah, but you don't know why they're actually answers to the questions
smoky panther
but im not here to learn the philosophy of math
frosty spoke
you can't tell me that if you don't know what f(4) - f(0) means that you can meaningfully answer anything
smoky panther
i just need to answer the one question, that is my goal
frosty spoke
this isn't the philosophy of math
these questions are asked to test your understanding of the underlying definitions and concepts
if you just want the answer, you can say so, but then you should know that this is really no different than just copying an answer off the internet in terms of usefulness
smoky panther
but i dont want to be tested. I just want to complete the work. I appreciate you trying to help me understand, seriously. You've been the most committed person that has tried helping me on the server
but i just need the answer, and i need someone to lay out the steps to doing that while guiding me
frosty spoke
okay, if you just want an answer to the question
something to write on a paper
the average rate of change of the function is given by ((f(4) - f(0))/(4-0) = 16/4 = 4
smoky panther
if you just want the answer, you can say so, but then you should know that this ...
i completely understand that
frosty spoke
we know that f'(x) = 2x, and solving f'(x) = 2x = 4 gives x = 2. Therefore the answer to the question is the point (2, 4)
smoky panther
there's no more to it?
frosty spoke
why would there be
frosty spoke
one more thing I'll leave you with, you'll probably spend more time with this approach than actually just learning things properly to begin with
but it's your choice
smoky panther
thanks, but no need to be so concerned with my life
u got ur own to worry about
.close
opal cradle
The product of the roots of the equation 3kx^2−qx−9=0 is −3 and their sum is 4 if k= and q=
In case you don't understand, I have to find the value of k and q
obtuse pebbleBOT
The product of the roots of the equation 3kx^2−qx−9=0 is −3 and their sum is 4 i...
high lily
what have you tried
opal cradle
I have searched in youtube how to resolve it, how to find the value of k in other exercises, and nothing
If it helps, the options of the value of k and q could be:
high lily
look up sum and product of roots
opal cradle
look up sum and product of roots
I have already searched but it doesn't give me any information which could help me with this exercise
high lily
it should have
using that info should lead you to setting up two equations
one for the info given about the sum of roots
opal cradle
it should have
Yes, but I couldn't find it yet and I have been searching for an hour, so I decided to ask for help here
high lily
and another for the product of roots
it'll pretty much be in the first one or two paragraphs of any documentation about sum and product of roots
opal cradle
it'll pretty much be in the first one or two paragraphs of any documentation abo...
Everything is about finding the value of x and y, not about another letters, or its product and its sum
high lily
can you show me what you're reading...?
opal cradle
can you show me what you're reading...?
It's in spanish, it doesn't matter?
opal cradle
high lily
so yeah
the main part to take from that is
for
$$ax^2 + bx+c=0$$
sum of roots
$$x_1 + x_2 = \blue{-\frac ba}$$
product of roots
$$x_1x_2 = \red{\frac ca}$$
you don't need to worry about finding $x_1$ or $x_2$
warm shaleBOT
ℝamonov
high lily
the expressions (in terms of k as q) for the sum and products can be obtained from the given quadratic
and you are also given their numerical values
opal cradle
and you are also given their numerical values
Okey, so what should I do first?
high lily
identity the a,b,c values in your quadratic
opal cradle
a= 3k
b= -q
c= -9
opal cradle
All right
high lily
now, with those expressions you just wrote
what is
-b/a
opal cradle
q/3k
opal cradle
Okey
high lily
and from the stuff above and in the link you had, this is the sum of roots
for which you are told the numerical value is 4
which allows you to make the equation
q/(3k) = 4
does that make sense so far?
opal cradle
k=1/12q
high lily
doesnt answer my yes/no question
opal cradle
doesnt answer my yes/no question
I understand that I should do that equation, but I don't understand what should I do about the sum of roots
high lily
wdym i literally just told you
the application of the sum of roots is the thing that gives you that equation in the first place
that's all that was done
and that's all I'm asking about atm
opal cradle
Oh, yes yes, I understand that part
high lily
now, apply the same idea and get another equation for the product of roots
opal cradle
now, apply the same idea and get another equation for the product of roots
-9/(3k)=-3
Is that okey? @high lily
opal cradle
-9/(3k) = -3
You're right, sorry, so now what should I do with these equations?
high lily
well
-9/(3k) = -3
is an equation with a single variable,
solving that will give you the value of k
opal cradle
well
> -9/(3k) = -3
is an equation with a single variable,
solving that will giv...
1
And for the value of q?
high lily
use your other equation from earlier
q/(3k) = 4
in addition to the value of k you just found
opal cradle
use your other equation from earlier
> q/(3k) = 4
in addition to the value of k ...
Thank you so much Ramonov, you're the best <3
Have a nice day and thanks for explaining me all this, seriously, thank you 
.close
strange yoke
obtuse pebbleBOT
strange yoke
How would I solve for this? It doesn't give me what the x coordinate is but it gives me the y
warm canopy
How would I solve for this? It doesn't give me what the x coordinate is but it g...
You need to solve x³ + x + 1 = 3 for x
strange yoke
find f'(x)
3 is the y value,I think I need to find the x value that goes with it and plug that in to f'
timid silo
o
warm canopy
Yes
strange yoke
Just test some easy small numbers
How do i test them?
warm canopy
Plug them in
obtuse pebbleBOT
Available help channel!
lucid salmon
(1/4a - a^3 - 3) + (2a^3 -1/2a^2 + 8)
obtuse pebbleBOT
(1/4a - a^3 - 3) + (2a^3 -1/2a^2 + 8)
lucid salmon
The sum would be a^3 - .5a^2 + .25a +5 right
lucid salmon
Is it not ok
muted delta
Use fractions if they are given to you
lucid salmon
Ok ig
muted delta
Use them
obtuse pebbleBOT
distant fulcrum
one way to check would be to sub in your value for F and work out the force going towards the right and see if you achieve equilibrium with the frictional force
do you know the formula to work out the frictional force?
@timid silo
yup
try and match this with the horizontal component of your worked out force
quartz mortar
I'm still confused on question 25. Does anyone know the equation for this one?
distant fulcrum
I'm still confused on question 25. Does anyone know the equation for this one?
are you familiar with suvat equations?
quartz mortar
yes
distant fulcrum
what is the value for s?
quartz mortar
the value for s is displacement
distant fulcrum
yh in this question what is the displacement of the coin being dropped
quartz mortar
11.4 meters?