i could only tell because you posted the answer
#help-27
near trout
if (x-3) is a factor, p(3) = 0
if p(3) = 0, (x-3) is a factor
so one thing you can do is just try like p(1), p(2), p(3), p(-1), all the common stuff to see whether it works out
silk ridge
i could only tell because you posted the answer
If I didn't, how would you try to solve it?
silk ridge
so one thing you can do is just try like p(1), p(2), p(3), p(-1), all the common...
I see
near trout
actually for this one i would probably start with p(3) and p(-3)
because you see it's got a 27 in
so it should be a factor of 27
silk ridge
after discovering that x-3 is a factor, what do I do?
near trout
polynomial long division
actually easier than regular long division
since you don't have to carry anything
look it up, you can learn it in like 30 mins tops, it's very simple
you just divide p(x) by (x-3) and that gives you the other bit
patent marsh
For abstract algebra
devout snowBOT
For abstract algebra
patent marsh
THIS IS NOT A VALID PROOF, just jotting down some ideas
I feel like I'm getting close but I'm not sure where to take it from here. Advice?
.close
hasty plaza
can someone please help me with a question
devout snowBOT
can someone please help me with a question
hasty plaza
so the question is
consider the function f(x) = x to the power of three + 4x^2 + kx - 4. The remainder from f(x) divided by (x+2) is twice the remainder from f(x) divided by (x-2). Determine the value of K.
.close
split copper
was doing a straightforward question about l'hopital's rule and ran into some issues when I put things into calculators... desmos seems to be dividing by 0 and getting a real answer.
for f(x)=sin(4pix) and g(x)=2cos(3pix), why does desmos show that at x=0.5, g(x)/f(x) = 1.5?
I'd think that since sin(4pi(0.5)) =sin(2pi) = 0 is in the denominator it would be undefined which also plays into the entire question i'm answering.
Also I might just be inputting it incorrectly but I swear I've looked at this for 10 minutes now and can't see anything wrong with it.
devout snowBOT
was doing a straightforward question about l'hopital's rule and ran into some is...
split copper
also i'm only in calculus 2 so if you could keep it to a level I could understand I'd greatly appreciate it 😅
hybrid snow
What's the original limit
hybrid snow
Summation AC moment
wooden veldt
The grey points are like points of interest not necessarily on the graph
wooden veldt
Desmos is whack, trust your gut
north light
quick question, say im factoring 8x - 12, would i take out a positive 4 or a negative 4?
devout snowBOT
quick question, say im factoring 8x - 12, would i take out a positive 4 or a neg...
covert pendant
positive 4
long kettle
Doesn't matter
covert pendant
since 8x is positive
long kettle
You can factor anything, technically
north light
and say i wanna put 3x+4 to 0
long kettle
It'd just get weird with different things
north light
would x = -4/3 or 4/3?
covert pendant
Doesn't matter
yeah true, I prefer not having negative x though
covert pendant
would x = -4/3 or 4/3?
it's -4/3
north light
could u explain why?
north light
bc in order for -4/3 to equal 0 doesnt x have to be pos 4/3?
or does it not work that way for fractions
covert pendant
no because if x = 4/3, you would just get a larger number
3 times 4/3 is 4, and if you add 4 to that you get 8
covert pendant
yes
devout snowBOT
@north light Has your question been resolved?
covert pendant
Factoring out a pos 1 doesnt do anything, since 1 times anything is itself
If you wanted to factor out somethin, -1 would probably be better
So it would be -1 (x + 3)
devout snowBOT
@north light Has your question been resolved?
bitter night
Can anyone teach me these
devout snowBOT
Can anyone teach me these
bitter night
<@&286206848099549185>
trim vine
Can you be more specific?
sacred plaza
which part
devout snowBOT
@bitter night Has your question been resolved?
bitter night
Can you be more specific?
Can you help me with
-5-6=?
It says -11
But I'm getting a different answer
-5-6= -5+(-6)=-1?
@sacred plaza
Just a little confused
Never mind
Got it
opaque mirage
<@&286206848099549185> yoohoo 👁️
woven radishBOT
Alpha Kappa
charred pebble
then just simplify the RHS
opaque mirage
rhs?
opaque mirage
i would get xi^2 - 25, would i then plug in 509 for xi^2 and solve through?
charred pebble
i would get xi^2 - 25, would i then plug in 509 for xi^2 and solve through?
you sure you would get xi^2 - 25 😅
opaque mirage
not anymore 
charred pebble
(a - b)^2 =
opaque mirage
ohhhh okay yeah i see, so it would be xi = 81, and (81-5)^2?
charred pebble
no no
you have studied identities like
(a+b)^2 =
(a-b)^2 =
(a^2 - b^2) =
stuff like that
you remember those?
opaque mirage
apparently not!
woven radishBOT
Alpha Kappa
opaque mirage
do these identities have some sort of name? so i can find and memorize them
charred pebble
idk but google says "standard algebraic identities"
charred pebble
i would get xi^2 - 25, would i then plug in 509 for xi^2 and solve through?
try this now
opaque mirage
**Alpha Kappa**
okok, following this, i get xi^2 + 25 - 2(xi)(5), which would then become 509 + 25 -25(81)
charred pebble
no dont go too fast
step by step
$\sum^n_{i=1}y_i=\sum^n_{i=1}(x_i^2+25-10x_i)$
woven radishBOT
Alpha Kappa
charred pebble
now here you apply one of the properties of summation
do you have the list of properties
or do you remember them?
opaque mirage
i do have 4 of 'em... one of them says you would pull out the 25 bc it's a constant
charred pebble
we will do that but not in this step
charred pebble
i do have 4 of 'em... one of them says you would pull out the 25 bc it's a const...
send them if you can
right
now looking at it
can you tell what we should use first
or needs to be used right now
we have something of the form sum (a+b+c)
what should we do next
opaque mirage
third property, right? the one where you separate all three terms into three separate summations?
opaque mirage
latex?
charred pebble
$\sum^n_{i=1}y_i=\sum^n_{i=1}(x_i^2+25-10x_i)$
can you type this?
opaque mirage
nope
charred pebble
ok i will do it then
$\sum^n_{i=1}y_i=\sum^n_{i=1}x_i^2+\sum^n_{i=1}25-\sum_{i=1}^n10x_i$
woven radishBOT
Alpha Kappa
charred pebble
is this right?
opaque mirage
yup!
opaque mirage
apply prop 1 to the one in the middle, 25
charred pebble
right
opaque mirage
prop 2 to the last one
charred pebble
can you tell me what it will become so i can type it
opaque mirage
yeah, given n = 20, it'll be 20(25) = 500
charred pebble
ok and the last one?
opaque mirage
would i use the given for xi, where it's equal to 81?
charred pebble
yeh thats the last thing to do
after applying 1 to second term and 2 to third term
you will get
$\sum^n_{i=1}y_i=\sum^n_{i=1}x_i^2+25n-10\sum_{i=1}^nx_i$
woven radishBOT
Alpha Kappa
charred pebble
then just put the given values and you are done
opaque mirage
ohh... apply the properties, then plugging in the numbers, it would become 509 + 25(20) - 10(81)?
charred pebble
yep
opaque mirage
yoooo thank you!! i wouldnt have gotten all of that on my own, i appreciate the step by step help
opaque mirage
on it
ok well, i applied one of the standard algebraic identities and got sigma(xi^2 + yi^2 + 2(xiyi)), then i separated all three terms via the third property on my notes
is that correct so far?
charred pebble
yep
opaque mirage
nice.. at this point im confused about the 1/n that's in front of all of the givens since i dont have those in what i have right now
opaque mirage
im guessing i now plug in the numbers, so it would now be 30 + 27 + 2(22)?
charred pebble
keep the 1/n in check
the given things are
1/n (sum xi) = something
and you to plug in the value of (sum xi)
so you will have to remove the 1/n from LHS first
opaque mirage
which means i would have to multiply the rhs by n, yeah?
charred pebble
yes
opaque mirage
so, (30 + 27 + 2(22))(n) would be it
charred pebble
yes
opaque mirage
ayeee thank you!!!
charred pebble
np 👍
opaque mirage
.close
restive river
devout snowBOT
restive river
How is this found after step 1
radiant drift
devout snowBOT
devout snowBOT
Available help channel!
restive river
Problem of the Day: The difference of two numbers is 37. The sum of the two numbers is 227;
what are the two numbers?
devout snowBOT
Problem of the Day: The difference of two numbers is 37. The sum of the two numb...
rocky iris
oh ok
restive river
i need help w this ques
rocky iris
Imma help
restive river
yea it may seem easy lol
restive river
mhm
rocky iris
Problem of the Day: The difference of two numbers is 37. The sum of the two numb...
and according to the questions, you can make a equations out of this
give it a go
restive river
oh ok lemme try
indigo river
132 and 95
restive river
.close
devout snowBOT
devout snowBOT
zenith jacinth
with intuition
no, algebraically there is a formula
try to look for it
but the best way to recognize the points is to draw it
ive never said that the formula for inflection point is the point of symmetry
A(a,b) is a point of symmetry if and only if his coordinates respect :
f(a-x)+f(a+x) = 2b
youve never seen that ?
read..
kinda
if a function is odd, then the functions has a point of symmetry
if its even, its an axis of symmetry
An example :
f : x --> x^2 is even and the y-axis is his axis of symmetry
not always...
and x^2 is never odd
x^3 + 2
:/
,graph x^3 + 2
,w x^3 + 2
stone stump
No that's neither odd nor even
zenith jacinth
yes
And thats why i was talking about intuition
I dont think so
if you know that the function is odd, at least you know that there is a point of symmetry
stone stump
Well b=f(a) so you could try solving that equality for a
long kettle
If f(a - x) + f(a + x) = 2b, it seems the x's should cancel for the LHS, no? Otherwise it might not equal 2b for all x
devout snowBOT
@deep vortex Has your question been resolved?
lapis valve
Is this 0 or 0.5
devout snowBOT
Is this 0 or 0.5
lapis valve
winter patrol
explain your reasoning that lead to two different values
devout snowBOT
@lapis valve Has your question been resolved?
winter patrol
were there any parts of what you did that you were unsure about?
lapis valve
No
winter patrol
which method did you use
winter patrol
wdym by "solve it"
what specifically did you solve
lapis valve
Is it right
winter patrol
can you show the work you did
lapis valve
I got it 0 and -4
winter patrol
why does it feel like you're never going to show the work i'm requesting
devout snowBOT
@lapis valve Has your question been resolved?
proud musk
I need to know how to calculate the primitive function of sin(x)*√cos(x)
proud musk
Not sure if primitive function is the correct term in english but basically opposite of derivative function
devout snowBOT
@proud musk Has your question been resolved?
proud musk
<@&286206848099549185>
Ok wait i didnt mention what i have tried already well i looked at my formulas and googled some extra formulas but im stuck because the primitive function of fg doesnt equal te primitive function of fthe primitive function of g
And therefor im stuck idk what to do i think i have to reform it somehow so i only have one thing sin cos or tan but idk how
I simply just need a little push in the direction and i think i can figure it out
Hmm tough one
gentle estuary
Integral?
proud musk
Ye
Im doing integrals and to calculate the area you need to find the primitive function first or however it is called in english
proud musk
Wait wait wait lemme find it back in my book we learned about that
OH WAIT YOU MEAN WITH u
gentle estuary
Any variable
proud musk
Ow ye i know that
gentle estuary
Yeah, what's the derivative of cos x?
proud musk
Ok wait i think i know it now u=sinx right
gentle estuary
Close
proud musk
Wait cos x
gentle estuary
-sqrt(u)
proud musk
Why minus?
proud musk
Omg im confusing primitive with dera thingy
Ok i understand now how can i close this ticket
gentle estuary
.close
pulsar folio
where did the minus sign went in the third step 😅
devout snowBOT
where did the minus sign went in the third step 😅
lunar harbor
where did the minus sign went in the third step 😅
typo prolly
,w sin^2 3A(1-sin^2 A)-cos^2 3A sin^2 A=sin^2 3A-sin^2 A(cos^2 3A sin^2 3A)
woven radishBOT
pulsar folio
and sin^2(a) - sin^2(b) = sin(a + b).sin(a - b)
what happened to cos²2A.sin²A
pulsar folio
no I checked it's not
pulsar folio
i was only simplifying a part of the numerator
it's alright
celest tide
what happened to cos²2A.sin²A
ah it gets cancelled in the last step lol
pulsar folio
but where did the - (negative sign) disappeared to in the third step, it became multiplication 😭
celest tide
thats a typo
pulsar folio
not only the negative sign disappeared but also the farthest right sin²A became sin²3A
celest tide
sin^2(3A) + cos^2(3A) is what it should have been
pulsar folio
sin^2(3A) + cos^2(3A) is what it should have been
no you don't get that when you cross multiply
pulsar folio
where did the minus sign went in the third step 😅
these half ass solutions on the internet sucks man
celest tide
no you don't get that when you cross multiply
you do
celest tide
these half ass solutions on the internet sucks man
solve it on your own, you should get the final result
high nebula
to prove a point is left differentiable and right differentiable at a point c, i just need to prove it's differentiable at a point c, right?
devout snowBOT
to prove a point is left differentiable and right differentiable at a point c, i...
scarlet sequoia
to prove a point is left differentiable and right differentiable at a point c, i...
yes
you mean function is differentiable at a point*
devout snowBOT
This look good
twin harbor
last ter mshoud le be()^2
twin harbor
ok ty
grim agate
np
devout snowBOT
@twin harbor Has your question been resolved?
devout snowBOT
twin harbor
This look ok so far?
devout snowBOT
Available help channel!
copper obsidian
I need a refresher if possible
devout snowBOT
I need a refresher if possible
copper obsidian
where do I begin?
for local maximum I got 1 by m=-3-1/1-5
And minimum by looking at the graph which I gues I could have done. So just need help with finding increasing and decreasing
devout snowBOT
@copper obsidian Has your question been resolved?
devout snowBOT
@copper obsidian Has your question been resolved?
copper obsidian
devout snowBOT
@copper obsidian Has your question been resolved?
devout snowBOT
@copper obsidian Has your question been resolved?
violet wind
What's the total change from 2001 to 2004?
devout snowBOT
@copper obsidian Has your question been resolved?
broken pawn
I was wondering if I factored out the square root correctly. And if it's possible to take out the -4 from the square root
devout snowBOT
I was wondering if I factored out the square root correctly. And if it's possibl...
@broken pawn Has your question been resolved?
broken pawn
.close
devout snowBOT
devout snowBOT
Available help channel!
old silo
i got a question
devout snowBOT
i got a question
old silo
in differential equation y^2 - 4y = 4e^-2x, do you count 4 as a polinome?
one partical solution is 4 and the other is e^-2x? or is everything just one partical solution?
lapis cargo
This is a separable DE and can be solved as such. But your question is a bit confusing I must admit, everything is included when solving and nothing is disregarded. I believe that’s the essence of your question
devout snowBOT
@old silo Has your question been resolved?
civic python
.close
devout snowBOT
Available help channel!
warped crest
Hey guys I have a question about combinatorics
devout snowBOT
Hey guys I have a question about combinatorics
warped crest
So I have 6 items, where 3 have one duplicate (ex aa,bb,cc)
And I want to choose 2 from this list, and I don't care what order these two are in (ie ab = ba
Combinatorics formula is nCr = n! /((n-r)! X r!)
That X is multiplication
What is the answer ? I thought it would be (6!) / ((6-2)! x 2! × 4), but that is wrong
Answer is 6 btw, I just don't know how to get there
bleak tide
That X is multiplication
This isn't an answer to your question, but often * is used for multiplication when typing, because x is commonly a variable
warped crest
Thanks, I was thinking * as exponential, but I guess ^ is
visual spire
And I want to choose 2 from this list, and I don't care what order these two are...
Two of the list to get what?
devout snowBOT
@warped crest Has your question been resolved?
devout snowBOT
@warped crest Has your question been resolved?
devout snowBOT
@warped crest Has your question been resolved?
lucid oracle
I have to find the common points of the equations 2x^2 + 2y^2 = 5 and xy = 1, how do i go about this?
devout snowBOT
I have to find the common points of the equations 2x^2 + 2y^2 = 5 and xy = 1, ho...
random temple
set y=1/x and plug it into the first equation
lucid oracle
damn i feel stupid now haha
thanks! i'm gonna try and solve it but meanwhile i'll keep the channel open in case i run into more questions
.close
real swallow
I need to find out where ”2x - 3y + 3 = 0” and ”3x - 2y = -1” intersect.
Its to graphs and I need to find out where they intersect with eachother.
Out teacher said we should be able to solve it without drawing a graph, but instead using g(x) = f(x)
devout snowBOT
I need to find out where **”2x - 3y + 3 = 0”** and **”3x - 2y = -1”** intersect....
real swallow
I typed them into desmos, but I need to solve it by myself, because it’s not allowed on tests
tame palm
They are both linear equations meaning that if they intersect they will only intersect in one location.
rough valley
To find where 2 functions intersect, we can set them equal to eachother
real swallow
So (2x - 3y + 3 = 0) = (3x - 2y + 1 = 0)?
rough valley
So **(2x - 3y + 3 = 0)** = **(3x - 2y + 1 = 0)**?
Set the second equation also equal to 0
Just add 1
rough valley
2x - 3y + 3 = 3x - 2y + 1
real swallow
Thank you mr gigachad
rough valley
ye
real swallow
x = 2 -y
How does this tell me where they intersect
I still have 2 unknowns right?
real swallow
2x - 3y + 3 = 3x - 2y + 1
Can I get an intersection point with 2 unknowns
rough valley
you can try system of equations
are you familiar with that?
not sure how your instructor wants you to do it, but you can solve a system
tame palm
You created a two-variable function, f(x,y) and g(x,y).
rough valley
try this: set one of the equations = to x and one = to y
rough valley
yea
rough valley
you can do that
you can also get one equation in terms of x and one in terms of y then plug in
such that you will get a single equation in terms of x
tame palm
When you made f(x,y) = g(x,y), you made a system of equations in an R^3 Euclidean graph.
The intersection is the line that you came up with.
You want to solve the problem for an R^2 Cartesian coordinate system.
\begin{align*}
2x - 3y +3 &= 0\
-3y &= -2x - 3\
y &= \frac{2}{3}x + 1
\end{align*}
woven radishBOT
Kookiemon
tame palm
\begin{align*}
3x - 2y + 1 &= 0\
-2y &= -3x - 1\
y &= \frac{3}{2}x + \frac{1}{2}
\end{align*}
woven radishBOT
Kookiemon
tame palm
Now you can set the two equations equal to each other.
$\frac{2}{3}x + 1 = \frac{3}{2}x + \frac{1}{2}$
woven radishBOT
Kookiemon
devout snowBOT
@real swallow Has your question been resolved?
real swallow
Thank you so much 🙏
glossy temple
18x - 18 = 5x - 10
devout snowBOT
18x - 18 = 5x - 10
glossy temple
should i transpose 5x to (-5x) if i will change it to the other side and combine it to 18x?
random temple
yes
glossy temple
.close
devout snowBOT
dire forge
yes, I think usually instead of writing $-$ for sets though, we write $(-2, 2) \setminus \left{\pm \frac\pi2\right}$
woven radishBOT
"Eric" Tao ("he"/him)
topaz umbra
devout snowBOT
topaz umbra
How do I do this?
quaint citrus
R u taking calculus?
Also are u allowed to use a graphing software or is it meant to be solved algebraically
topaz umbra
so derive and set to 0?
quaint citrus
Ye
topaz umbra
i have alot of e^x
not sure where to go from this or if I even did it right
can i show u
quaint citrus
Well the first step is right
The big fraction
Wait a sec
Try the distributing part again
-(e^x)(2x-4)
quaint citrus
I’m not too sure what ur referring to, I recommend starting from the big fraction and simplifying again
topaz umbra
I have this
Where should I go from here if correct
Oh I see
Do u cancel out the e^x
And solve for x?
I see I got the correct answer
Thank you very much Stephen
.close
supple cove
devout snowBOT
supple cove
im doing book problems
im confused on how you get to the final answer
does the derivative of theta sin (theta) become just cos (theta)
hollow pollen
derivative with respect to theta?
are you familiar with the product rule @supple cove
hollow pollen
and youre asked to find the derivative of
$\theta^{2} \sin{\theta}$
$\dfrac{d}{d\theta} \theta^{2} \sin{\theta}$
woven radishBOT
Gijs
supple cove
yeah
devout snowBOT
trim vine
Eyo whatup
Wait u want problem 32?
Ok hmm
Inside the square root, multiply by 1+sin(x) / 1+sin(x) cuz then the denominator will becomes a difference of squares
That’s one thing to notice: trig proofs love difference of squares* cuz they love squares
After all, there are squares in the Pythagorean identity sin^2 + cos^2 = 1
Tell me what u get
hybrid snow
If there's a |cos(x)|, somewhere in the denominator of the radicand it becomes cos^2(x)
trim vine
If there's a |cos(x)|, somewhere in the denominator of the radicand it becomes c...
One thing I don’t understand is why the cos is absolute valued but the 1 + sin isn’t?
winter patrol
consider the range of 1+sin(x)
trim vine
[0,2]
hybrid snow
It's unnecessary to have the absolute value if its always nonnegative
trim vine
Ahhh
hybrid snow
technically it's supposed to be |1+sin(x)| but it's like
winter patrol
*non negative
hybrid snow
Useless
winter patrol
don't feel the urge to always expand everything
hybrid snow
winter patrol
no, you don't
trim vine
don't feel the urge to always expand everything
Because square stuff can do stuff when it’s inside a square root
hybrid snow
Just multiply the radicand by $\frac{1+\sin(x)}{1+\sin(x)}$
woven radishBOT
Umbraleviathan
winter patrol
it's perfectly fine to leave (1+sin(x))^2 as it is in your intermediate work
winter patrol
you do NOT need to explicitly expand that
hybrid snow
So like it's useless to expand if you're gonna compress it again
We're just watching
List the steps out
trim vine
I left cuz too many cooks in the kitchen
winter patrol
if you insist on multiplying out the numerator despite us saying it's unnecessary (and inefficient), sure
hybrid snow
Just leave the numerator as (1+sin(x))^2
Your teacher's an idiot if he's like "oh you gotta expand it"
You should only expand it if it's necessary
Lol
.close
restive river
.close
restive river
,w (-2i)^3 * (-3i)^2 = -1(-2)3(-3)^2
livid star
how answer in my book is -72i?
woven radishBOT
Requested by zela#5879
restive river
,w (-2i)^3 * (-3i)^2 = -1(-2)3(-3)^2
woven radishBOT
restive river
It's false
livid star
What is i^3
-i
livid star
i typed -1 by wrong
restive river
i^3 would be 1
trim vine
Also (-1)^3 is -1
hybrid snow
i^3 would be 1
That's also just wrong lol
hybrid snow
i typed -1 by wrong
You should know i tends to behave cyclically.
i^1 = i
i^2 = -1
i^3 = -i
i^4 = 1
And it repeats
livid star
ok but if we did i*i will be -1
livid star
so i get i from -2's brace and i get i from -3's braces and i put it outside brackets
so -1 * ...
i do not have i^3 at anyway
it is i^2 so will be -1
so i made -1(-2i)^3 (-3)^2
so it will be 72
hybrid snow
My guy
livid star
how answer in my book is -72
hybrid snow
You should know i tends to behave cyclically.
i^1 = i
i^2 = -1
i^3 = -i
i^4 = 1
_ _
Let's break it down
$$\begin{align*}
(-2i)^3(-3i)^2 &=(-2)^3(i)^3(-3)^2(i)^2 \
&= (-8)(-i)(9)(-1) \
&= -72i
\end{align*}$$
woven radishBOT
Umbraleviathan
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hybrid snow
@livid star again, i^3 = -i
livid star
ok now i got it
hybrid snow
I shouldn't need to repeat myself like 3 times
livid star
thx bro it helps me a lot
livid star
I shouldn't need to repeat myself like 3 times
i know i^3 = -i , i am just can not understand steps
.close
ashen garden
hi, my problem is i need to find the point of intersection (lines with conics) of the equation x^2+y^2=25 and a line x+y=1
foggy snow
hi, my problem is i need to find the point of intersection (lines with conics) ...
try to find where there x and y coords are equal i guess?
ashen garden
ok
devout snowBOT
@ashen garden Has your question been resolved?
latent jackal
are the factors of 120=8x+2x^2
x=6 and x=-10
midnight dirge
idk just
plug in the als
n dont take up multiple channels
,calc 120=8x+2x^2 where x=6
woven radishBOT
The following error occured while calculating:
Error: Invalid left hand side of assignment operator = (char 4)
midnight dirge
,calc 8x+2x^2-120 where x=6
woven radishBOT
The following error occured while calculating:
Error: Invalid left hand side of assignment operator = (char 20)
midnight dirge
,w 8x+2x^2-120 where x=6
woven radishBOT
midnight dirge
,w 8x+2x^2-120 where x=-10
woven radishBOT
devout snowBOT
midnight dirge
also use 1 channel
latent jackal
also use 1 channel
oh ok
midnight dirge
devout snowBOT
Available help channel!
bright gulch
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bright gulch
For number 47, do i have to use long division here?
long kettle
I would
broken pawn
yes since the numerator degree is larger than the denominator degree
remote meteor
- divide
- split integral
- set up for pfd
- split again
- u sub
- simplify
- sub in values
devout snowBOT
@bright gulch Has your question been resolved?
acoustic sky
Hey can anyone help me with u substitution derivatives?
devout snowBOT
Hey can anyone help me with u substitution derivatives?
acoustic sky
Going through a problem and keep getting stuck
restive river
You should post your problem
remote meteor
,rotate
woven radishBOT
acoustic sky
Do I plug 4x^3+1 back in for U
And do I find the antiderivative of that
and that's the answer?
remote meteor
Ye progressing good
remote meteor
Raise it to 1/2
acoustic sky
the (4x^3+1)^1/2
remote meteor
Sqrtu to u^1/2
remote meteor
Then by power rule , integral of u^1/2 with respect to u is 2/3u^3/2
Simplify it and replace all instances of u with 4x^3+1
acoustic sky
Is this legal? :
devout snowBOT
Is this legal? :
woven radishBOT
acoustic sky
k
acoustic sky
or am i doing the antiderivative there wrong
remote meteor
By power rule , integral of u^-2 with respect to u is -u^-1
woven radishBOT
acoustic sky
so here
on the last step can I bring the 1/x^1/2 out?
devout snowBOT
@acoustic sky Has your question been resolved?
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@acoustic sky Has your question been resolved?
fringe nacelle
Pls help on 2)
devout snowBOT
Pls help on 2)
fringe nacelle
Tried doing this
amber valley
I think you first translate it then rotate clockwise 90deg
fringe nacelle
How do u get an equation from that
amber valley
For the translation you have y=f(x+1)-1
fringe nacelle
Okay so u have
y = f^-1 (x+1) - 1
or
x = f(y + 1) - 1
The answer key says “ y = f^-1 (-x -1) - 1 “
amber valley
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topaz portal
tanx+cotx=3,
what is the positive value for sinx-cosx?
devout snowBOT
tanx+cotx=3,
what is the positive value for sinx-cosx?
topaz portal
i did that but couldnt find anything idk
inland seal
well you can solve for x
grim agate
first we solve tan and cot equation
yes
thats idea
can you explain it to them
i gtg
okay @topaz portal
do you get what i said
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young torrent
Umm my teacher never taught me this ;-; can someone explain and tell the answer
pseudo basin
malicious compliance would be to write $\paren{\frac{25}{36}}^1$
woven radishBOT
Ann
umbral creek
malicious compliance would be to write $\paren{\frac{25}{36}}^1$
HAHA
pseudo basin
this problem is not very well written. it admits multiple possible answers with no clear way to tell what was meant
grim agate
quaint citrus
But there is an answer that is the most obvious lol
It seems as if the point of the question is to get that answer
wispy flume
Nah bro
pseudo falcon
Uh the answer should be (5/6)^2 i guess
wispy flume
The most obvious solution is to the power 1
pseudo falcon
Well yes
wispy flume
,, \paren{\frac{25}{36}}^1
woven radishBOT
gracialglacier
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woven radishBOT
gracialglacier
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wispy flume
bruv
i spent an hour on maths
ona dumb question
and i deal with a rude texit bot
great just great
grim agate
@wispy flume \paren isn’t defined macro in latex
wispy flume
<@1015865096729284698> \paren isn’t defined macro in latex
then how tf did miss ann over here do it
this texit showing favouritism
im reporting
grim agate
they have it defined in their preamble
mental merlin
Hello how can I prove that it is true? P is the amount of the numbers that are relatively prime with a number. For example 120 = 2^3 * 3 * 5 and the amount of the relatively prime numbers is 2^3 * 3 * 5 ( 1- 1/2)(1-1/3)(1-1/5).
devout snowBOT
Hello how can I prove that it is true? P is the amount of the numbers that are r...
@mental merlin Has your question been resolved?
mental merlin
<@&286206848099549185>
burnt peak
yes?
mental merlin
Hello how can I prove that it is true? P is the amount of the numbers that are r...
.
devout snowBOT
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devout snowBOT
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zenith wyvern
I'm stuck, I can't find anything on the intenet about this formula : U(n)+1 = U(n)^2 + a I wanna convert it to an explicit formula but I have no idea how. If anyone knows the final result, I don't really care about explanations.
devout snowBOT
I'm stuck, I can't find anything on the intenet about this formula : U(n)+1 = U(...
plush knot
What do you mean by explicit? what do you want to isolate, u, n or a?
zenith wyvern
I want U(n) in function of n
plush knot
oh ok mb
zenith wyvern
not U(n+1) in function of U(n)
devout snowBOT
@zenith wyvern Has your question been resolved?
zenith wyvern
<@&286206848099549185>
devout snowBOT
@zenith wyvern Has your question been resolved?
devout snowBOT
@zenith wyvern Has your question been resolved?
restive river
I'm stuck, I can't find anything on the intenet about this formula : U(n)+1 = U(...
quadratic formula¯_(ツ)_/¯
restive river
im studying polar coords
devout snowBOT
im studying polar coords
restive river
a little confused here
what is the vector equation
for a 2d cartesian vector the equation is $v = a\hat i + b\hat j$
woven radishBOT
metnal
restive river
is it $v = a\hat r + b\hat \theta$ for a polar vector?
woven radishBOT
metnal
restive river
where \hat r and \hat theta are the base vectors
because i saw it written as $r-\theta$
woven radishBOT
metnal
restive river
im not sure what this denotes
restive river
to my understanding Cylindrical coordinate system is just a vector space
is that correct?
wooden veldt
what do you mean by "coordinate system is just a vector space"?
restive river
take the 2d Cylindrical coordinate system
i mean the polar 2d grid
isnt it just a vector space of the 2nd dimension?
restive river
but is the 2d polar grid a vector space?
wooden veldt
R^2 is a vector space, polar coordinates are a coordinate system on R^2
coordinate systems are distinct from a basis
restive river
im sorry this doesnt make sense to me
isnt a coordinate system basically a basis?
i mean
we can construct coordinate systems that arent bases?
ok nevermind
i should probably get back to my original question
apparently a basis can form a coordinate space but not every coordinate space is a basis, i think..
anyway thanks
.close
devout snowBOT
wooden veldt
apparently a basis can form a coordinate space but not every coordinate space is...
this is correct yes
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Available help channel!
lament raven
I dont understand this at all
lament raven
forgot to close last lmao
lament raven
I dont understand this at all
I know how to do DA ik how to do Klygenes into Dueseldorfs but I dont get Klygenes/Seilas into Widget/Dueseldorfs
verbal kindle
just DA with stupidass unit names
What is DA?
devout snowBOT
@lament raven Has your question been resolved?
heady silo
devout snowBOT
heady silo
I do not know what to times together
umbral creek
ef is 21
and bf is 12
you can use the formula where a and b is 21 and 12
to find c
which is BE
heady silo
thank you
umbral creek
no prob!
heady silo
.close
mild basin
devout snowBOT
mild basin
Why are these values not included?
They are the x intercepts so wouldn’t they belong in the inequality?
mild basin
Oh
umbral creek
if so then your inequality would be $\leq$ I think
woven radishBOT
duckiescute!
devout snowBOT
umbral creek
no prob!
devout snowBOT
Available help channel!
rough sparrow
devout snowBOT
arctic field
amazing
midnight dirge
u know P B|A
arctic field
lets not just throw in a formula without explaining where it comes from
midnight dirge
wow
arctic field
because bayes is just a simple consequence of the conditional probability formula
rough sparrow
Mmm
arctic field
bayes isnt a central part of probability
midnight dirge
with that u can find P B
arctic field
you only think of bayes when you machine learning
but machine learning puts too much emphasis on it
midnight dirge
ahem
midnight dirge
sob
arctic field
use conditional probability formula directly
midnight dirge
so many images
rough sparrow
So A intercept B = 1/2* 1/8
arctic field
seems legit
devout snowBOT
@rough sparrow Has your question been resolved?
rough sparrow
How would A’ work
woven radishBOT
arctic field
the main thing is calculating the numerator
and the way to do that is to realise that
woven radishBOT
arctic field
also called the total probability formula
its basically saying if you're in B, then you're either in B and A, or youre in B and not A
rough sparrow
(2/16)/(13/16)?