Yes
#help-10
restive ridge
ivory flare
Tbh American curriculum sucks + my own school's fault
pine sail
- your own
restive ridge
^
ivory flare
At any rate, what
restive ridge
"my school didn't teach me that" is never an excuse in mathematics
ivory flare
+ your own
Factual
pine sail
At any rate, what
You agreed to the 9w^2 - 108 = 9w didn't you?
ivory flare
You agreed to the 9w^2 - 108 = 9w didn't you?
Yess
ivory flare
What you can do that? Isn't w² treated as a different term than w
pine sail
w is different from w^2.
When did I even claim they are the same?
9w^2 - 108 = 9w
9w^2 - 108 - 9w = 9w - 9w
Is what I said.
ivory flare
Waitt you're basically simplfying 9w² and 9w?
swift marsh
If you have an exam tomorrow I think you probably just have to try and go back over some of the earlier stuff you saw
Seems like there’s a fundamentals problem
ivory flare
If you have an exam tomorrow I think you probably just have to try and go back o...
I understand my notes and most of what the teacher explained but its this weird worksheet
swift marsh
I mean exam tomorrow or not tbh
ivory flare
Seems like there’s a fundamentals problem
With logarithms or quadratics?
swift marsh
Well quadratics are like ultra fundamental maths
ivory flare
I don't know what I don't know if that makes sense
I don't know what topics i have no idea about like I thought I understood logarithms
swift marsh
Quadratics because if you can’t solve quadratics like this then probably there’s other things too
But it’s important to get them down
Watch a video on it
ivory flare
I think I'm getting confused with logarithms mashed with quadratics
ivory flare
Watch a video on it
Quadratics?
pine sail
Yes.
swift marsh
Well if confronted with the equation 9x^2 - 9x -108 = 0 can you solve it?
ivory flare
Ah okay but can you continue explaining after the subtracting?@pine sail
swift marsh
If not there’s a problem there
pine sail
Ah okay but can you continue explaining after the subtracting?<@7480296030873846...
Factor 9
Just solve the quadratic though.
It's either you can solve it or not.
If you can.
You're done here.
If you can't like dk.dkn suggested, watch a video.
ivory flare
Well if confronted with the equation 9x^2 - 9x -108 = 0 can you solve it?
I think so i just cant solve it quickly
It'll take me more than a few secs
pine sail
You can solve it VERY quickly by factoring
ivory flare
Just solve the quadratic though.
Okayyy got youu
You'll end up with something like 9w-108 right?
swift marsh
No
You simply factor it (after dividing by 9 probably)
Factoring is something you should know how to do, if you don’t, it’s fine, but you should go and learn about it
ivory flare
What are you dividing by 9 again?
swift marsh
Yes
swift marsh
Ohhh i just didn't understand the -1 guy
I mean they seemed to explain it perfectly fine
Besides you have to be able to solve it even if you can’t factor it as easily as that
For example you should be able to solve 6x^2 + 7x + 2 = 0
ivory flare
Okay now that i reached w²-w-12 i found solution steps
Whats this called though? Like the topic
Like is there a specific name for this
swift marsh
Factorisation of quadratics
ivory flare
Aren't there a lot of ways to factor? Like using the formula
There's no like specific thing that pertains to that specific quadratic?
ivory flare
Like yeah I guess
swift marsh
That specific quadratic? Not really what’s so special about it
ivory flare
This is so weird I could've sworn I fully understood quadratics
swift marsh
Factorisation is separating it into factors, i.e brackets
Solving it using the formula isn’t really factorisation
timid silo
factorization is basically splitting a function into constituent divisors of the function, it helps you predict the zeroes in quadratic equations
ivory flare
Btw, when we're working with an x² in a logarithmic equation, it means we have 2 solutions right?
swift marsh
Btw, when we're working with an x² in a logarithmic equation, it means we have 2...
Not necessarily
Possibly
Also depends on whether you consider complex-valued logarithms or not
pine sail
After you split the middle term you do factorisation by grouping terms.
Also just because there is an x^2 does NOT mean 2 solutions.
swift marsh
ln(x^2) = ln(x^2 + 1) has zero solutions for example
ivory flare
Also depends on whether you consider complex-valued logarithms or not
I do yeah
timid silo
wait so you know complex numbers, roots of unity and not factorization
pine sail
Yes, that is how it is.
ivory flare
wait so you know complex numbers, roots of unity and not factorization
Not really
Kind of?
A lot of shallow knowledge in all
Um why is this wrong
ivory flare
Ohhh i think i messed up while multiplying the logs
timid silo
shouldnt it be x(x+4)=2^5
ivory flare
Oh how?
pine sail
$\log_2{x(x+4)} = 5$
warm shaleBOT
What the hell am I doing here?
pine sail
Any issues so far?
ivory flare
No
warm shaleBOT
What the hell am I doing here?
ivory flare
10²=x
100?
pine sail
Exactly.
pine sail
**What the hell am I doing here?**
Why can't you use the same idea here?
ivory flare
Oh wait I think i know where i messed up
pine sail
Now you do.
ivory flare
In another world
ivory flare
Oh but im confused as to how it turned to 2⁵
Oh wait
No im not?
I think i need to rest
Im gonna close this thank you for the help
.close
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
trail haven
At a birthday party, a guest has to launch a rocket. The height of the rocket above the ground can
described with the quadratic function f (x) = -2x
2 + 8x where f is the height of the rocket in meters above
the ground and x are the lateral distance from where the guest is firing the rocket.
a) How far from the point of launch does the rocket hit the ground?
b) How high does the rocket reach the highest? Use algebraic solution to solve the problem.
obtuse pebbleBOT
At a birthday party, a guest has to launch a rocket. The height of the rocket ab...
trail haven
i got A) to 4, is that correct? And how would I procceed with B)?
solar igloo
At a birthday party, a guest has to launch a rocket. The height of the rocket ab...
you mean
-2x² + 8x
?
then A is correct, it's the x intercept.
B is your maximum.
trail haven
yeah sorry i mean that yh
how do I figure out the maximum? Or is the maximum the same as the A?
solar igloo
A is when it hits the ground
your ground-intercept 😄
B is the highest point. So you either need the vertex form or derive it
drowsy girder
axis of symethry : 
trail haven
im on 0 hours of sleep so my brain is not responding well
trail haven
B is the highest point. So you either need the vertex form or derive it
enlish isnt my first language, but how would that look like
english
solar igloo
we have 3 different methods to solve this problem, now.
i'm not sure which one you use in school?
vertex, derivative, axis of symmetry
drowsy girder
Derive - a verb for proccess differentiation
trail haven
Derive - a verb for proccess differentiation
let me just google transelate that
yh we def use axis of symmetry
drowsy girder
$$\frac{-b}{2a}$$
warm shaleBOT
Pluton
drowsy girder
$f(x) = ax^2 + bx + c$
warm shaleBOT
Pluton
trail haven
and x is 4?
drowsy girder
We dont care about x
trail haven
alright
drowsy girder
This is a function
drowsy girder
Did you plug in b and a in -b/2a
trail haven
so 8x/2(-2x)?
is the answer 2?
or should i use 2 in the equation?
so the maximum is 8?
ive been left for my stupidity
drowsy girder
so the maximum is 8?
Yes
worn yacht
can you use the exponent derivative rule to do derivatives of a number like 4x?
warm shaleBOT
Umbraleviathan
fierce lagoon
what do you do with x?
look
worn yacht
what is x^0?
0
fierce lagoon
no
you remmever you exponent rules?
what happens when you raise anything to the 0 power
worn yacht
so 4(1)(1) = 4
so you multiply it by the zeroth power?
fierce lagoon
hold on
fierce lagoon
**Umbraleviathan**
Look
If you recall the exponenent rule
$\frac{d}{dx}Cx^n = Cnx^{n-1}$
C =4, n = 1 in your case
warm shaleBOT
Umbraleviathan
fierce lagoon
C =4, n = 1 in your case
worn yacht
C =4, n = 1 in your case
where did c come from?
drowsy girder
what is x^0?
1 for x ≠ 0
worn yacht
1 for x ≠ 0
oh
worn yacht
C is like the k I showed you earlier
ohh
worn yacht
C =4, n = 1 in your case
ok
fierce lagoon
1 for x ≠ 0
I mean like
For derivatives i mean
I mean
that shit dont matter :troll:
I dont have nitro anymore i gotta remember that
worn yacht
I dont have nitro anymore i gotta remember that
lol
drowsy girder
Thats why i kinda hate power rule for linear equations
Its not x^0 because that doesnt work for all x
worn yacht
I mean like
so what do you do next?
fierce lagoon
Quite literally use the power rule
fierce lagoon
**Umbraleviathan**
this
Im gonna highlight the C (lime) and n (blue) parts in colors
${\color{lime}{4}}{\color{cyan}{(1)}}x^{{\color{cyan}{1}}-1}$
$\frac{d}{dx}{\color{lime}{C}}x^{{\color{cyan}{n}}} = {\color{lime}{C}}{\color{cyan}{n}}x^{{\color{cyan}{n}}-1}$
worn yacht
<@953140475693514804> see?
yes
worn yacht
<@953140475693514804> see?
so can you write the steps down
worn yacht
the steps are:
1. use formula
lol
sour wagon
Calculate the distance from point X to line segment AB. X(13,4) A(1,14) B(2,0). I think I don't know how to apply the distance formula. I was able to solve something similar to this just because the two points of A and B were 0 so the answer was Xy.
obtuse pebbleBOT
Calculate the distance from point X to line segment AB. X(13,4) A(1,14) B(2,0). ...
cedar lichen
How do you define the distance from a point to a line?
sour wagon
d=|axX + byX +c|/rad(a^2+b^2)
timid silo
How do you define the distance from a point to a line?
The perpendicular distance
cedar lichen
Oh, we got a whole ass formula. I was planning on deriving it, but if you know a formula, that's fine.
cedar lichen
The perpendicular distance
I know, I was asking as a probing question
sour wagon
Oh, we got a whole ass formula. I was planning on deriving it, but if you know a...
I mean whatever is easier lol
cedar lichen
Probably the formula, if you know how to use it
sour wagon
Probably the formula, if you know how to use it
Usually when I had this formula I was expecting something like ax+by+c=0
cedar lichen
As the equation of the line?
sour wagon
yeah I think so
cedar lichen
Then find the equation of the line
Wait, did you mean ax + by + c = 0?
Not ax + bx + c = 0
sour wagon
a yeah sorry messed up
timid silo
a yeah sorry messed up
Find the slope using the given points
Then use it to get the equation of the line
sour wagon
I know this might sound weird but I wasn't taught math in English. Could you show me or explain what you define by slope?
timid silo
I know this might sound weird but I wasn't taught math in English. Could you sho...
It's not weird, it's alright
The general equation of a line can be represented as y=mx+c. Here, m represents the slope or tangent of the angle of the line. Slope can be calculated using (y2-y1)/(x2-x1) where (x1,y1) and (x2,y2) are two points on the line.
sour wagon
fking finally. I searched in 2 languages for the equation but nothing came up on the internet 🤣
I think this is what I was searching for
Pro tip: After your finals never throw all your notebooks away :)))
timid silo
Pro tip: After your finals never throw all your notebooks away :)))
True that
sour wagon
It's not weird, it's alright
The general equation of a line can be represented ...
I got -14
timid silo
I got -14
So y=-14x+c. Use one of the 2 points to get c and there you have your equation of the line.
sour wagon
So y=-14x+c. Use one of the 2 points to get c and there you have your equation o...
is c -28 by any chance?
timid silo
is c -28 by any chance?
I think it is 28
sour wagon
I think it is 28
+28 or -28?
timid silo
+28 or -28?
It's y=-14x+28, no?
sour wagon
I used the matrix method and I got 14x+y-28
timid silo
Satisfies A and B
timid silo
I used the matrix method and I got 14x+y-28
Yeah we're both correct
Just kept c on different sides
sour wagon
Yeah we're both correct
so now I have the slope, what would be the next step?
timid silo
so now I have the slope, what would be the next step?
Now you have the equation of the line in the form of ax+by+c=0. You already know the formula to get a distance from a point for this.
d=|ax0 + by0 + c|/sqrt(a^2+b^2)
Where (x0, y0) is the point from which distance is needed
sour wagon
d=|ax0 + by0 + c|/sqrt(a^2+b^2)
Where (x0, y0) is the point from which distance...
if there is no b then it is 1?
cause it's just y
timid silo
if there is no b then it is 1?
Yeah, it means 1
sour wagon
d=|ax0 + by0 + c|/sqrt(a^2+b^2)
Where (x0, y0) is the point from which distance...
so the distance from point X to AB is then 1.08?
a forgot the radical
timid silo
so the distance from point X to AB is then 1.08?
I haven't calculated it myself but if you applied the formula correctly, it'd be alright
timid silo
a forgot the radical
We call it square root here, which I denoted by 'sqrt'
sour wagon
ah yeah, I get 214/sqrt(197)
I think this is it
according to wolfram also
thanks !
.close
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
wicked tundra
why did the interval change?
obtuse pebbleBOT
why did the interval change?
nocturne minnow
why did the interval change?
It made the interval in terms of u
wicked tundra
It made the interval in terms of u
oh so how do I understand that algebraically
nocturne minnow
Do you understand u sub in general?
obtuse pebbleBOT
@wicked tundra Has your question been resolved?
heady vessel
hello
heady vessel
how to find equation of y=f(x) graphically
and also using that same graph to show the point(s) where the gradient of y=f(x) is 1/2
obtuse pebbleBOT
@heady vessel Has your question been resolved?
high lily
what have you tried?
heady vessel
i have some working
but i do not understand it
im not sure how to approach this question
heady vessel
how to find equation of y=f(x) graphically
that is working for this question^
valid crown
find roots
then scale for peaks
from just lloking you should guess it will look like this:
valid crown
y =a×x×(x+b)×(x-b)
heady vessel
but it needs to me solve it graphically
heady vessel
oh
valid crown
apparently at 1.2
high lily
seems that based on the work they did, they had some pre-knowledge of the function
heady vessel
ohh i see i see
valid crown
so you wind up
heady vessel
square root?
valid crown
yeah
valid crown
because you'll use this:
(a+b)×(a-b) = (a^2 - b^2)
in this case
(x-sqrt(1.2))*(x+sqrt(1.2))
high lily
no
heady vessel
no?
high lily
why are you using 1.2 or sqrt 1.2
valid crown
so sqrt(12)
heady vessel
wait why is it 12
valid crown
wheres 12 coming from
first formula in the picture
high lily
heady vessel
3.46
high lily
which is approximately sqrt(12)
valid crown
yeah so 12 = 3.46^2
heady vessel
i am so so so sorry im so lost again
valid crown
but choose this because it's x value is not complicated
heady vessel
im really horrible at maths
heady vessel
local min/max
so -2. 1.6 and 2,-1.6
valid crown
that you see to hqve easy values
valid crown
so -2. 1.6 and 2,-1.6
yeah I guess
heady vessel
so we just sub in x for 2?
heady vessel
wait
valid crown
is this 2 or squared
it's just a×2
heady vessel
i am so so sorry what are we subbing it into again
actually it is ok i ask another for help
sorry for bothering you
how to close channel
.close
willow ravine
Complex Variables question:
obtuse pebbleBOT
Complex Variables question:
gusty hinge
obtuse pebbleBOT
gusty hinge
I keep getting -25x^2/16y^3 instead of -25x^2/16y^2 for the final answer. Am I doing something wrong?
nocturne minnow
Looking at the key you posted, this here, it somehow canceled a y in the second fraction, which is not correct. The denominator is still 4y^2
nocturne minnow
Meaning what you have, should be right
gusty hinge
Ah thank you, I wasn't sure as for the second part of the question, it worked off the answer it got
.close
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
candid ingot
Hi,can anyone help me with this? Is it need to find all of their y=mx+c
obtuse pebbleBOT
Hi,can anyone help me with this? Is it need to find all of their y=mx+c
timid silo
opposite sides of a rhombus are parallel
candid ingot
means FG=EH?
timid silo
length wise yes,
but the relevant sides here are FE and GH
and the important part is parallel, not magnitude
candid ingot
How I find the q tho
timid silo
by using the fact that the two lines in the question are parallel
vast willow
Hi
royal basin
does rational root theorem help at all?
192 looks like a number with a lot of factors.
vast willow
does rational root theorem help at all?
What's that
It's the first time which I try to solve such equations
royal basin
,w rational root theorem
warm shaleBOT
royal basin
or for a TL;DR
given a polynomial equation whose coefficients are all integers,
if it has a root that is a rational number, then it is a number of the form ±(divisor of constant term)/(divisor of leading coefficient).
in this particular case, the leading coefficient is 1 so the search space for rational roots reduces to only those which are integer divisors of 192.
vast willow
Ok but shouldn't it work too by factoring
royal basin
there are 5 terms
factoring 'directly' would require you to know to split one of the terms in two
deft thicket
u could break one up and make two squares
vast willow
I tried by taking x^3 as a common between the first 2 variables and then tried to factor other terms alone to get at last a common between all but that didn't work
royal basin
figuring that out is, at best, nontrivial
you are going down a route that is more complicated than necessary.
vast willow
That's bc I don't know other ways
royal basin
i gave you the name of another way
vast willow
I'll try to use that
royal basin
i described it to you in brief but full detail
vast willow
Thank you so much
royal basin
ok
vast willow
I am trying to solve this just for fun and to know how to solve more complicated equations
I saw someone sending this question but no one answered him so I tried to solve it bc maybe i could answer him but I couldn't
deft thicket
well id suggest u broke up 4x^2 in order to get a common factor
but how is the question
wait i think i found it juct a sec
solved it
real roots are 4 and 3
and imaginary are +-4i
vast willow
Look I tried splitting-16x into -4x-12x where I took common factor between 4x^2 and -4x to get 4x(x-1) and I took a common between -12x and -192 but I didn't get a result that helps me continue on
deft thicket
16*
vast willow
Not 192
deft thicket
oops
deft thicket
yes its 12
vast willow
Yes
deft thicket
and then u take common factor and solve it
vast willow
Wait lemme try
deft thicket
ive solved it it works
deft thicket
real roots are 4 and 3
those are the roots
vast willow
Ik but I want to reach the steps to learn the concept
deft thicket
ok do u need help with that?
vast willow
Did u take a common factor between -x^3 and x^4?
deft thicket
ye and -12x^2 do u want to send u my work?
vast willow
Yes if u pls
deft thicket
ok just a moment
deft thicket
ur welcome
vast willow
You take 16 common between 16x^2-16x-192 and took x^2 as a common between x^4-x^3-12x^2
vast willow
It becomes (x^2-x-12)(x^2+16)
deft thicket
ye
vast willow
Yes but that's after you told me the most important step in solving it
deft thicket
ye
obtuse pebbleBOT
deft thicket
u too
rancid halo
!close
cyan thistle
10a?
cyan thistle
unsure what to do
half venture
unsure what to do
cyan thistle
is answer
cyan thistle
where did x-6 come from?
hexed agate
they subtracted 3 and 3 from x?
half venture
the entire side is x.
the two 3cms are understood right?
the middle side would be x - 3 + 3
timid silo
Shouldn't the CDF of p(6) be greater than one?
obtuse pebbleBOT
Shouldn't the CDF of p(6) be greater than one?
royal basin
is "p(6)" meant to be P(X <= 6)?
timid silo
is "p(6)" meant to be P(X <= 6)?
Yes, I am sorry.
timid silo
Is it allowed to assign a proposition to another proposition without logical connectives?
obtuse pebbleBOT
Is it allowed to assign a proposition to another proposition without logical con...
frosty river
What do you mean with "assign"?
timid silo
what else could that be?
frosty river
? I'm trying to help, sorry for not being a native English speaker.
Can't you rephrase your question of give an example of what you are trying to do?
timid silo
with assign i mean, is it possible that a proposition inherits its bivalent value from the bivalent value of another proposition?
obtuse pebbleBOT
@timid silo Has your question been resolved?
steep harness
with assign i mean, is it possible that a proposition inherits its bivalent valu...
Can you give an example using symbolic notation? If I understand you correctly, propositions inherit their truth value (if that's what you mean by bivalent value) through inference rules, often implications
(A→B)→(P→Q)
"A implies B" implies "P implies Q."
The former implication holding then logically means that the latter holds.
timid silo
So, is that only possible if there's a premise?
steep harness
It's hard to imagine there not being a premise involved. Could you give an example of a possible counterexample? I'm still not sure if I'm fully understanding what you're trying to do.
peak hamlet
If the median = (n+1)/(2)
obtuse pebbleBOT
If the median = (n+1)/(2)
peak hamlet
How does this make sense
The median of this data
The answer makes sense when just visually solving the question but I don’t understand how (n+1)/(2) applies to this
obtuse pebbleBOT
@peak hamlet Has your question been resolved?
fluid snow
Find all prime factors of $3^{18} - 2^{18}$.
\
$$3^{18} - 2^{18}$$
$$= (3^9 + 2^9)(3^9 - 2^9)$$
$$= (3^9 + 2^9)(3^{4.5} + 2^{4.5})(3^{4.5} - 2^{4.5})$$
$$= (3^9 + 2^9)(3^{4.5} + 2^{4.5})(3^{2.25} + 2^{2.25})(3^{2.25} - 2^{2.25})$$
$$= (3^9 + 2^9)(3^{4.5} + 2^{4.5})(3^{2.25} + 2^{2.25})(3^{1.125} + 2^{1.125})(3^{1.125} - 2^{1.125})$$
$$\vdots$$
obtuse pebbleBOT
Find all prime factors of $3^{18} - 2^{18}$.
\\
$$3^{18} - 2^{18}$$
$$= (3^9 + 2...
warm shaleBOT
Kepe
fluid snow
But how do I know which of them are prime?
kind hawk
most of them aren't even integers
fluid snow
yeah
kind hawk
you can't just continue to half the exponents
fluid snow
oh
kind hawk
there are ways to factor a^3+b^3 and a^3-b^3
fluid snow
Why should I look at it as a difference of cubes rather than difference of squares though?
How would I know that from the start?
Because 9 is odd and when halved will produce roots?
kind hawk
yeah that should be the start to realize that you need a different approach to go further
and after squares there are cubes
so just the next step
fluid snow
$$3^{18} - 2^{18}$$
$$= (3^6 - 2^6)(3^{12} + 6^6 + 2^{12})$$
warm shaleBOT
Kepe
steep harness
I think splitting it into two differences/sums of cubes is a bit easier to deal with to start
fluid snow
Oh, now I can split (3^6 - 2^6)
high lily
you could start either way
fluid snow
I think splitting it into two differences/sums of cubes is a bit easier to deal ...
wdym
high lily
3^18 - 2^18 could be considered as both a difference of two squares and a difference of two cubes
steep harness
It stays as a binomial longer and gets down into smaller powers before you expand into trinomials
fluid snow
yeah
fluid snow
It stays as a binomial longer and gets down into smaller powers before you expan...
You mean using $(3^6 - 2^6)(3^{12} + 6^6 + 2^{12})$ instead of $(3^9 + 2^9)(3^9 - 2^9)$?
warm shaleBOT
Kepe
steep harness
Other way around, but yeah
fluid snow
oh
high lily
if you approached it as a difference of two squares
after getting
(3^9 + 2^9)(3^9 - 2^9)
you'd consider sums and differences of two cubes
steep harness
It's easier to factor binomials than trinomials generally
fluid snow
you'd consider sums and differences of two squares
oh, to get integral exponents you would use sum or difference of cubes after that
high lily
sry typo
fluid snow
$$3^{18} - 2^{18}$$
$$= (3^9 + 2^9)(3^9 - 2^9)$$
$$= (3^3 + 2^3)(3^6 - 6^3 + 2^6)(3^3 - 2^3)(3^6 + 6^3 + 2^6)$$
warm shaleBOT
Kepe
fluid snow
Now I should split $3^3 - 2^3$ into differences of cubes again, right?
warm shaleBOT
Kepe
steep harness
You certainly can
Once you get down low enough you can just start crunching the numbers
fluid snow
$$3^{18} - 2^{18}$$
$$= (3^9 + 2^9)(3^9 - 2^9)$$
$$= (3^3 + 2^3)(3^6 - 6^3 + 2^6)(3^3 - 2^3)(3^6 + 6^3 + 2^6)$$
$$= (3^3 + 2^3)(3^6 - 6^3 + 2^6)(3 - 2)(3^2 + 6 + 2^2)(3^6 + 6^3 + 2^6)$$
warm shaleBOT
Kepe
steep harness
Now you can split 3³+2³ into sum of cubes
fluid snow
Now there is one more sum of cubes and after that, there isn't much more I can do, right?
fluid snow
$$= (3^3 + 2^3)(3^6 - 6^3 + 2^6)(3 - 2)(3^2 + 6 + 2^2)(3^6 + 6^3 + 2^6)$$
$$= (3 + 2)(3^2 - 6 + 2^2)(3^6 - 6^3 + 2^6)(3 - 2)(3^2 + 6 + 2^2)(3^6 + 6^3 + 2^6)$$
warm shaleBOT
Kepe
steep harness
Notice that these trinomials can be rewritten as sneaky binomials
fluid snow
$$= (5)(7)(577)(1)(19)(1009)$$
warm shaleBOT
Kepe
steep harness
Now you only have to check 577 and 1009 for primeness, which is much easier
Only have to check for primes up to 30 for 577, and... Less than 40 for 1009
fluid snow
alr, thx!
$$577 \equiv 5 + 7 + 7 (mod 3)$$
$$577 \equiv 1 (mod 3)$$
$$577 \equiv 2 (mod 5)$$
$$577 \equiv 500 + 70 + 7 (mod 7)$$
$$577 \equiv 3 (mod 7)$$
$$577 \equiv 5 (mod 11)$$
$$577 \equiv 5 (mod 13)$$
$$577 \equiv 16 (mod 17)$$
$$577 \equiv 7 (mod 19$$
$$577 \equiv 2 (mod 23)$$
$$577 \equiv 26 (mod 29)$$
that was a pain lol
warm shaleBOT
Kepe
fluid snow
So 577 is prime
fluid snow
Only have to check for primes up to 30 for 577, and... Less than 40 for 1009
Why do I only have to check up to 30?
steep harness
Because if there are no prime factors less than √577, then there can't be any greater than that either, and 30²=900, which is an easy approximation to check that only gives you about 3 extra primes
fluid snow
Because if there are no prime factors less than √577, then there can't be any greater than that either
Why is this?
oh, because anything greater than it would require a factor smaller than it to become 577 and there are none because we checked the primes up to it?
steep harness
Yes
It's an easy fact to remember, but kinda hard to rigorously explain lol
It's like how if you have a sum a+b=x s.t. a<b; a≤x/2
It's how the factors pair up. It's a beautiful fact to remember that makes checking for primeness = π(√x) in number of operations
(pi being the prime counting function)
fluid snow
It's like how if you have a sum a+b=x s.t. a<b; a≤x/2
Hm, some of these facts kinda make sense intuitively but I still can't really understand them rigorously lmao
fluid snow
It's how the factors pair up. It's a beautiful fact to remember that makes chec...
yeah, probably very useful for programming
thank you, I will check 1009 for primeness then
.close
bold mural
obtuse pebbleBOT
timid silo
what is the remainder theorom?
what does it state?
what do u understand by remainder theorom
u should also use factoring btw
proven zephyr
u should also use factoring btw
why not just use remainder theorem without factoring?
timid silo
why not just use remainder theorem without factoring?
factoring makes calculations super easy
u can use $(a+b)^3=a^3+3a^2b+3ab^2+b^3$
warm shaleBOT
∆y/∆x=πy+π^2x
timid silo
that makes it really easy
ye
timid silo
explain in one line
what does it state simple as that
it isnt 3 pages long
u dont need to show examples or anything
timid silo
do you know what it is?
bold mural
do you know what it is?
The simplest definition is in the first page of the notes I send. Legitimately cannot think of something simpler
timid silo
The simplest definition is in the first page of the notes I send. Legitimately c...
let their be a polynomial $p(x)$ which i am dividing by $x-a$ whats the remainder
warm shaleBOT
∆y/∆x=πy+π^2x
timid silo
The simplest definition is in the first page of the notes I send. Legitimately c...
ur notes = not needed
whats needed is what u understand by it
timid silo
**∆y/∆x=πy+π^2x**
remainder in terms of a
bold mural
ur notes = not needed
whats needed is what u understand by it
Bruh I just understood my own notes and now I know the answer bruh. The answer is x = 1/2
timid silo
Bruh I just understood my own notes and now I know the answer bruh. The answer i...
no it isnt lmao
neither are u solving for x
in the orginal question
bold mural
no it isnt lmao
Oh fuck then it means I don’t understand shit
bold mural
no it isnt lmao
If you understand, can you tell me?
timid silo
let their be a polynomial $p(x)$ which i am dividing by $x-a$ the remainder is $p(a)$
warm shaleBOT
∆y/∆x=πy+π^2x
timid silo
this is what the remainder theorom states
the next is the factoring formula
$(a+b)^3=a^3+3a^2b+3ab^2+b^3$
warm shaleBOT
∆y/∆x=πy+π^2x
obtuse pebbleBOT
@bold mural Has your question been resolved?
hexed agate
f(1/2) is the remainder right?
hexed agate
using the factoring formula factor the cubic
Why do you need to factor?
Can't you just plug in x=1/2?
hexed agate
Ok in this example it's easy but most of the time it's not easy to factorize cubes
harsh plaza
Isnt this a sinple case of taking the absolute of the square root of each side?
harsh plaza
Because symbolab doesnt seem to agree with me
hasty crag
yeah you can take the square root on both sides and then just solve for x
just double checking, this is the equation right? $(0.5 + 2x)^{2} = 49(0.2 - x)^{2}$
warm shaleBOT
texaspb
hexed agate
What did symbolab say?
|0.5+2x| = |7 * (0.2 - x)|
Case 1: 0.5+2x = 7(0.2-x)
Case 2: 0.5+2x = -7(0.2-x)
,w |0.5+2x| = |7 * (0.2 - x)|
warm shaleBOT
hexed agate
,w (0.5+2x)^2 = (0.2-x)^2 * 49
warm shaleBOT
warm shaleBOT
hexed agate
,w 0.5+2x = -7(0.2-x)
warm shaleBOT
hexed agate
What sis symbolab disagree with @harsh plaza
obtuse pebbleBOT
@harsh plaza Has your question been resolved?
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
midnight crater
obtuse pebbleBOT
midnight crater
I got 8 i want someone to confirm if thats the answer since I'm not sure
royal basin
,calc (-8/2 + 12 * 9 - 4 * 6)/(56/7 * 2)
warm shaleBOT
Result:
5
How
high lily
how are you getting 8
midnight crater
I made some corrections but let me show u my work
The part where I put 112 i made that correction rn
warm shaleBOT
Result:
5.5
..?
high lily
well -4 + 108 = 104
was correct
your edit just now resulted in something wrong
high lily
you're confusing addition with subtraction
midnight crater
where?
high lily
well before that edit it seemed that you had
104 - 24
and somehow that resulted in 128 which is actually 104 + 24
high lily
well that's supposedly what you did in your head
you have no indication of 104 - - 24 on the page
in your table you had
104
+- 24
midnight crater
I do its there i just put a + where the - was in blue pen
high lily
yeh...my point exactly
you have no indication of 104 - - 24 on the page
you had 104 + - 24
midnight crater
Isn't 104 - - 24 = 104+24?
midnight crater
you had 104 **+** - 24
That plus was a minus but I changed it to a plus
high lily
why did you change it to a +
midnight crater
Two negatives= positive?
high lily
where's two negatives coming from
midnight crater
-
- 24
high lily
whut
midnight crater
104- - 24
high lily
i still don't see how you're getting that 2nd negative
lets break down the numerator into smaller parts
-8/2 = -4 right?
midnight crater
-4×6=-24
high lily
12 * 9 = 108 right?
midnight crater
Yeah
high lily
-4 * 6 = -24 right?
midnight crater
Ye
midnight crater
Yes
high lily
do you agree that -4 + 108 is equal to 104
midnight crater
Yes
midnight crater
Oh 104-24=66?
high lily
no
midnight crater
80
high lily
where the heck is 66 coming from
midnight crater
lol I did it badly in my head
high lily
yes, 104 - 24 = 80
(and i still don't have any idea how you generated a second negative)
high lily
structure your work more clearly
you're doing too much scratchwork on the side to have a clear idea of where stuff goes
high lily
you just wrote - - 24
and i still have no idea how you got that second negative
tell me exactly what you're doing to get - - 24
high lily
where's here
midnight crater
-8÷12 + 12×9 - 4 x 6
high lily
that's still valid so far
midnight crater
the minus acts both as a negative and a minus or?
high lily
you could view it as the subtraction of 4*6
or the addition of (-4*6)
$-8\div 2 + 12\times 9 \red{+} (-4 \times 6)$
warm shaleBOT
ℝamonov
midnight crater
+-..? = to a minus or?
midnight crater
Positive and negative = negative
Negative and negative = negative
Right?
high lily
yes
Positive and negative = negative
if by "and" you mean +
then it depends and/or i don't really know what you mean with that vague wording
midnight crater
104+-24 = minusing or?
Thats where I'm confused
104-24=80
OHH
I get it now
high lily
subtraction of is the addition of the negative of
high lily
subtracting = adding a negative number
not quite
midnight crater
?
high lily
don't over simplify it
midnight crater
100+-20= 100-20 =80
high lily
you can subtract other things than positive numbers
e.g
subtracting -3 from 5
5 - (-3) = 5 + 3
which is NOT adding a negative number
midnight crater
Thats two negatives =positive/addition,
high lily
numbers aren't the only thing that can be subtracted either
sure you can express
5 - p as 5 + (-p)
but p is a variable and just because there's a - sign in front of it doesn't necessarily mean that -p is negative
certain things can be viewed in multiple ways
midnight crater
I was taught that the sign on the left of the number determined if it was negative or not a while back idk if it still applies
high lily
and the point that i'm trying to make is that
subtracting = adding a negative number
is oversimplified and i've just demonstrated how that's inaccruate
hence why i deliberately chose to use the negative of instead of a negative number
midnight crater
negative of instead of a negative number what is the difference?
high lily
subtracting -3 from 5
midnight crater
-2?
high lily
no
i'm typing
would you agree that
5 - (-3)
is an accurate representation of -3 being subtracted from 5
?
midnight crater
a negative number minus a positive number ??
high lily
not what i'm asking atm
midnight crater
-3-5 isn't it the same as 5- -3
high lily
no and still not what i'm asking
midnight crater
What are you asking?
high lily
would you agree that
5 - (-3)
is an accurate representation of -3 being subtracted from 5
its a yes/no question
midnight crater
uhh no cause 5 would remove the -3
high lily
wdym by remove
midnight crater
Its positive and bigger so it will be minusing it
high lily
don't know what you mean
midnight crater
idk either its just something I remember being taught
midnight crater
like write the equation for it or?
high lily
write the expression
midnight crater
5-2
midnight crater
5-1
high lily
-3 being subtracted from 5
following the exact same structure you're applying there gets you
5 - (-3)
or 5 - - 3
i deliberately inserted parentheses to make things clearer
this being subtracted from 5 can be represented as
5 - this
it doesn't matter whether this is positive or negative or 0
midnight crater
Subtract -5 from 3
3 - (-5)
Like this?
high lily
different values to what i set up but yes
and following the rules of - * - → +
that gets you
3 + 5
midnight crater
I'll have to read up on the foundations so I don't mix them up
high lily
which is the addition of a positive number (5) and not a negative number as you described in your oversimplification
the difference is the negative of what you're subtracting in this case -5 is indeed 5
midnight crater
ah ok
well ty for the help atleast ill be able to answer the first question on the paper correctly now
obtuse pebbleBOT
@midnight crater Has your question been resolved?
hexed blaze
Hi...
obtuse pebbleBOT
@hexed blaze Has your question been resolved?
obtuse pebbleBOT
@hexed blaze Has your question been resolved?
fleet onyx
how do i do the second part? the (x-2)^k is throwing me off
obtuse pebbleBOT
how do i do the second part? the (x-2)^k is throwing me off
fleet onyx
am i able to just take it out as a constant even though its raised to the k
actually wait hold on i worked it out with the ratio test and i eventually ended up with |x-2| lim k->inf = 2
obtuse pebbleBOT
@fleet onyx Has your question been resolved?
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
obtuse pebbleBOT
tardy epoch
,w 20 choose 6
warm shaleBOT
tardy epoch
,w binomial coefficient
warm shaleBOT
obtuse pebbleBOT
timid silo
sounds like nim https://en.wikipedia.org/wiki/Nim
wait, surely the optimal move is to take everything from pile 1 if you are the first player if n is odd
if n was even, the players wont even interact, right?
well if n is even, then on turn n, player 2 takes from pile n, and on turn n+1, it goes back to p1 taking from pile 1
nim is usually more complex
it's sufficient here to consider the case of n even/odd
try the game with 2 piles yourself and see what happens
didn't you say they have to follow the order of the piles? so from pile 1 to 2 back to 1
without that condition, the game becomes much more interesting (and analysing using nim would be useful)
they say that they must pick from the next pile in the list
there is no choice the players can make of which pile to pick from
Formally, if a player removed stones from pile i on a turn, the other player removes stones from pile ((i % n) + 1) on the next turn.
yeah
which part do you mean?
ig it's just interpreting the actual problem
highlighting important parts work well
and coming up with small examples
scarlet lantern
The temperature of a starbucks coffee after n minutes is given by T = 72(0.85)^n + 20 how long does it take for the coffee to cool to a temperature of 70 degrees
Hey for this question im just unsure where to start or what methods to use
obtuse pebbleBOT
The temperature of a starbucks coffee after n minutes is given by T = 72(0.85)^n...
cedar lichen
What have you tried
scarlet lantern
ive tried bringing the n down and using logs while subbing t for 70
cedar lichen
Show your work
scarlet lantern
ok hold on
https://cdn.discordapp.com/attachments/852642410570711050/990773241918390353/IMG_4637.jpg and then i divided it to try and get n by itself but when i subbed in the answer for n it wasnt right
sorry for the shadow
cedar lichen
,rotate
warm shaleBOT
cedar lichen
log(b^n) = nlogb, true, but that's not the case you have
72*(0.85)ⁿ is not the same as (72 * 0.85)ⁿ
So log(72(0.85)ⁿ) ≠ n log(72(0.85))
scarlet lantern
how would i do that by changing forms?
scarlet lantern
divide both sides by 72?
cedar lichen
Yes
scarlet lantern
i got 25/36 = 0.85^n
scarlet lantern
now we use the log to bring the n down?
cedar lichen
Yes
cedar lichen
Yep
scarlet lantern
got 2.24
cedar lichen
You could've also done something with log(75(0.85)ⁿ). This isn't relevant per se but I think it's good to know. You can turn that into log(75) + log(0.85ⁿ) = log(75) + nlog(0.85) as an alternative way to solve for n
scarlet lantern
oh thats cool
thanks for your help like i knew what i needed to do kind of but i was stuck
cedar lichen
Anyway, the answer is correct
scarlet lantern
do i need to do anything to close this?
cedar lichen
Type ".close"
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
hushed girder
hey can i get help on a question
obtuse pebbleBOT
hey can i get help on a question
nocturne minnow
hey can i get help on a question
hushed girder
i understood the 1st one but i dont understand what the power is for rolling a dice once
feral sedge
obtuse pebbleBOT
@hushed girder Has your question been resolved?
timid silo
Is this question possible to derivate?
obtuse pebbleBOT
Is this question possible to derivate?
timid silo
I'm getting stuck after taking power as 1/ln
I see, it must be an error.
Thanks
.close
dreamy forge
obtuse pebbleBOT
nocturne minnow
,rotate
warm shaleBOT
dreamy forge
Did I solve z correctly? How would I solve the other ones
Can I use Soh Cah Toa, Im not sure if its a right triangle im a lttle confused
@nocturne minnow
nocturne minnow
Please don't ping me
dreamy forge
ok
tranquil arch
Did I solve z correctly? How would I solve the other ones
correct, and you should write 30°, not just 30, and sin(30°)=1/2
dreamy forge
Got it thanks
For the other ones can I use SOH CAH TOA??
Its hard to tell if they are right triangles...
distant schooner
wiht questions like these it is largely right triangles
dreamy forge
So its safe to assume their right triangle