empty sapphire
yeah no problem! Hopefully that helped. If it helps to remember, the original function set the precedence for the domain, so if it gets simplified than we need to still use the same domain.
#help-28
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simple ridge
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simple ridge
how does the angle $\alpha <90$ becomes $90-\alpha$ upon transposition ( rotation 180 about the principal diagonal)
glossy valveBOT
calculus is fun
simple ridge
upon rotating 180 about the principal diagonal the 2 elements joined by this segment will interchange positions
so the slope will remain negative but how will the angle with the row become $90-\alpha$ with the row
glossy valveBOT
calculus is fun
simple ridge
shouldnt the angle stay $\alpha$ because the angle with the row after rotation will be vertically opposite with $\alpha$?
glossy valveBOT
calculus is fun
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simple ridge
<@&286206848099549185>
calm pasture
Am I doing something wrong here
full forumBOT
Am I doing something wrong here
calm pasture
Because I don’t know what my next step should be
vast fossil
Yeah but it's easier to use bounds of u
calm pasture
Because I didn’t plus in du/dx either
Is there a different way, because I don’t know how to do it the way you’re describing
vast fossil
Oh and yeah you forgot to divide by 2 after the sub
Okay can you recall the fundamental theorem of calculus
calm pasture
Oh and yeah you forgot to divide by 2 after the sub
At which step? Where I plugged in u right
vast fossil
Divide the whole function because du/dx = 2?
Yeah
vast fossil
At which step? Where I plugged in u right
When you rewrote everything with u, yes
calm pasture
1/2u^3?
vast fossil
yeah
vast fossil
So by the end it should be $\frac12\lim_{t\to\infty}\int_1^tu^{-3}\dd{u}$
glossy valveBOT
A Lonely Bean
vast fossil
Ok then what
Okay, so $\int_a^bf(u)\dd{u} = F(b) - F(a)$ as long as $F' = f$, right?
glossy valveBOT
A Lonely Bean
vast fossil
Alright
calm pasture
OH I GET IT
vast fossil
So everything's clear now?
calm pasture
sub in 1 and infinity to find the answer
vast fossil
Yup
vast fossil
You are welcome, close the channel if you have no other doubts/questions
calm pasture
.close
short bridge
Hello.
short bridge
I'd like a hint for this, please.
If $p$ and $p^{2} + 2$ are primes, show that $p^{3} + 2$ is prime.
glossy valveBOT
Enemagneto
short bridge
Just the HINT, please.
sharp vine
maybe
p^2 + 2 = p^2 - 1 + 3 = (p-1)(p+1) + 3
if p^2 + 2 is prime
what does that tell you about (p-1)(p+1)
short bridge
what does that tell you about (p-1)(p+1)
Well, that's clearly not prime.
sharp vine
in other words
short bridge
You mean composite ?
sharp vine
(p-1)(p+1) + 3 is prime, so it cannot be divisible by 3
short bridge
Oh yes.
sharp vine
and so (p-1)(p+1) cannot have a factor 3
short bridge
Yes
nova basin
Oh
short bridge
Wait.
nova basin
Nice
nova basin
I didn't push that one through but nice
short bridge
So, I can work this out after this ?
nova basin
Yes
short bridge
Okay. Thanks everyone.
short bridge
and so (p-1)(p+1) cannot have a factor 3
Does that mean that p is 3 ?
sharp vine
yes
short bridge
Oh.
So cool.
So, this is not true for any prime p other than 3?
I think so.
Basically, whenever p and p^2 + 2 are prime, we have by our method that p has to be 3.
stable plover
correct
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glad prairie
i have to calculate the derivate of
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i have to calculate the derivate of
spice orchid
you understand that the first line is just the multivariable chain rule?
glad prairie
hum no
i know the chain rule of a composite function but not that
ok i got what it is
just i don't get why it is y and not x
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@glad prairie Has your question been resolved?
torn jolt
where does the last part come from?
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where does the last part come from?
torn jolt
cos * the phase
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torn jolt
Does the tic tac toe method work with every integration by parts?
torn jolt
Ok so i better stick with traditional methods
quaint prawn
not necessarily
torn jolt
Like the ALPES method
quaint prawn
it is fine to try but you should be able to recogonize when it wont work
just choose a u and a dv manually
use that if you know it will go through
torn jolt
it is fine to try but you should be able to recogonize when it wont work
What is generally a sign it wont work?
quaint prawn
when applying IBP a finite amount of times wont get the solution
sleek apex
tic tac toe method 
quaint prawn
I honestly don't even know what tic tac toe method is, I just assume it is the same as DI method
sleek apex
i thought tabular method
sleek apex
is DI differentiation integration
quaint prawn
ye
sleek apex
yeah essentially tabular
silent vessel
trying to figure this page out, needing a little help, second photo is what i’ve done but i’m not sure if it’s right
placid oar
do you know what $f \circ g$ means?
glossy valveBOT
imTypθ
silent vessel
do you know what $f \circ g$ means?
more or less, my teacher just tought me it td
so i dont fully know it
placid oar
essentially, $f \circ g = f(g)$, in others words, put the whole g function inside the x of the f function
glossy valveBOT
imTypθ
silent vessel
hmm
placid oar
Do you think you can now do those problems?
placid oar
what do you want me to clarify?
silent vessel
**imTypθ**
this pretty much, its just a little bit confusing
silent vessel
okay!'
placid oar
[f(x) = x^2 ] [ g(x) = x+2 ] [ f \circ g = f(g(x)) = (x+2)^2]
i'm testing out stuff with color hold on xD
blegh
no color ig
glossy valveBOT
imTypθ
placid oar
Hopefully this makes it clearer for you
silent vessel
okay! so would the second picture that i put. was it the correct way to solve it?
placid oar
I think what you did was $f \cdot g$, not $f \circ g$
glossy valveBOT
imTypθ
placid oar
the empty circle means putting a function inside another, not multiplying
silent vessel
ahh ok
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shadow bridge
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onyx glen
they just wrote $(1 + \ln(x)^4)^{-1/2}$ as $\frac{1}{\sqrt{1+\ln(x)^4}}$
shadow bridge
I thought that when you multiply, numerators and denominators go to their respective places but why is numerator and denominator both on the bottom?
glossy valveBOT
Ann
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pseudo summit
pseudo summit
what happened to the 3p under "For q:
surreal hull
it is setting the partial derivative wrt q to 0 instead of the original expression
somber violet
you treat it as a constant
pseudo summit
you treat it as a constant
is there a rule for that?
light sonnet
That's how partial derivatives work
pseudo summit
like what if there was another similar equation
somber violet
yes
partial differentiation treats all other variables as a constant
(unless otherwise specified)
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nova wing
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nova wing
how do i do part b? i don't really understand it
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nova wing
<@&286206848099549185>
feral wolf
nova wing
i'm stuck on what to do after x=e^2y-6e^y+5
loud oak
f(x) = e^(2x) - 6*e^(x) + 5
Change f(x) to y
y = e^(2x) - 6*e(x) + 5
Swap the variables
x = e^(2y) - 6*e^(y) + 5
Now, Isolate y, lemme do this part on a paper
u can try it on your own as well
loud oak
you can use natural log "ln" to isolate y
loud oak
ln doesnt apply like this
you have to separate each part
try taking e^y common from all elements and see if that makes any difference
nova wing
what does that mean?
loud oak
f(x) = e^(2x) - 6*e^(x) + 5
y = e^(2x) - 6*e^(x) + 5
x = e^(2y) - 6*e^(y) + 5
x = e^(y) * (e^(y) - 6) + 5
trying to wrap my head around to find a solution\
if its not possible then just write the inverse is not possible
nova wing
this is the mark scheme
nova wing
how do u do that?
loud oak
you can make factors of it
like this
y = e^(2x) - 6*e^(x) + 5
y = e^(2x) - e^(x) - 5*e^(x) + 5
y = e^(x) * (e^(x) - 1) - 5 (e^(x) - 1)
y = (e^(x) - 1) * (e^(x) - 5)
close to making it a perfect square if I change the constant value
add 4 on both sides
make 5 into 9 and then its a perfect square
nova wing
wouldn't that be minus 4?
nova wing
thank you!
loud oak
it was a nice change of pace for me as well
im refreshing my maths skills now
well the inverse if 1 part of this
the main problem isnt solved yet
nova wing
theres the domain
loud oak
the value at which the inverse is not possible is x < -4
if x goes beyond -4 then the value inside the root becomes negative
which we dont want
nova wing
yep
loud oak
so its domain would be [-4 <= x <= positive infinity)
take note of the brackets as well
[ means the value is closed at -4 and it cannot go beyond it
nova wing
kk
loud oak
) means the other end is open and any value is acceptable around that end of the boundary
largest value for a can be positive infinity
and its inverse should still exist
loud oak
ahh +- for taking squareroot on both sides
i missed that part
now the domain changes
ypu that domain is correct
and largest value for a becomes 5
loud oak
infinity is an output which is acceptable
it would become a problem is a negtive value is inserted in ln
yea it was a fun problem
lemme know if you got more like these,
loud oak
sure
crystal cobalt
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crystal cobalt
(Group 1) X (Group 2)
X is the median element
so i was thinking if the highest value in group 6 was like 36000
then obviously median would be equal to that or higher
But then it wouldn't work because the average of group 2 would be higher than what is projected
wait it works omg
i thought i read 38000 as 36000 lol
wdym~
I don't do mental math lol
proper hawk
crystal cobalt
Anyway, change of question, that's my new question^
How would i do that?
for q=6 and n=6, i had 3^6/2^(24)
not sure if that is bigger than 1/18
tbh
oh bruh i keep misreading the question ughhh
okay nvm, q=6 and n = 6 gives 6/24 = 1/4 (i think) and that's bigger than quantity B
not sure how to generalize though
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stark ruin
not sure how to generalize though
because we have to check odd and even factors
write as
2^3q
so
2^3n x q^n
do you know how to get total number of factors?
will be (3n+1)(n+1) if q is prime
now u just gotta find out how many of the factors will have a power of 2 in them
crystal cobalt
do you know how to get total number of factors?
wdym?
okay i see the part about simplification
glossy valveBOT
hiii
crystal cobalt
what now?
stark ruin
this will be generally proved by induction then
firstly let q be prime not equal to 2
total factors
3n+1(n+1)
out of these
how many factors will be odd
those who dont have a factor of 2
so
here n+1 being the total odd powers
so n+1 out of all factors will be odd
n+1/3n(n+1)
thats 1/3n
its coming equal lool
stark ruin
n+1/3n(n+1)
similarly if q is product of 2 odd primes
total factors is
(3n+1)(n+1)(n+1)
odd factors come out to be
(n+1)(n+1)
and the cycle repeats
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@crystal cobalt Has your question been resolved?
crystal cobalt
its coming equal lool
idts it's equal
the answer is A
and yeah i understnad that the number of factors (total) is (3n+1)(n+1)
yeah i just checked the answer for you lol
it's definitely A
stark ruin
idts it's equal
Let me.find
My error
Number of odd factors is 1 p p² p³...
So n+1
N+1/(3n+1)(n+1) -(n+1)
N+1/3n (n+1
1/3n
Well this is awkward
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astral wyvern
i need some help with #2. im new to inverse logs
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i need some help with #2. im new to inverse logs
What step are you on?
1. I don't know where to begin
2. I have begun but got stuck midway
3. I got an answer but I'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above
@astral wyvern Has your question been resolved?
spiral vigil
it should be fairly similar to (1)
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normal thicket
47X=11 mod 249
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47X=11 mod 249
normal thicket
,w hcf of 47, 249
onyx glen
put a space after the comma
glossy valveBOT
onyx glen
wolfram thinks 47,249 means forty-seven thousand, two hundred and forty-nine
normal thicket
47X=11 mod 249
There must be a unique solution
onyx glen
and there is
onyx glen
well you could find the inverse of 47 mod 249 using the euclidean algorithm.
don't know how much time that'd take
zenith kernel
onyx glen
Goal: find 47^-1 mod 249
Using Euclidean algorithm on 249 and 47,
retracing steps to express GCD(47, 249) = 1 as a linear combination of 47 and 249
249 = 47*5 + 14
=> 14 = 47*(-5) + 249*1
47 = 14*3 + 5
=> 5 = 47*1 + 14*(-3)
=> 5 = 47*1 + 47*15 + 249*(-3)
=> 5 = 47*16 + 249*(-3)
14 = 5*3 - 1
=> 1 = 5*3 - 14
=> 1 = 5*3 + 14*(-1)
=> 1 = 47*48 + 249*(-9) + 47*5 + 249*(-1)
=> 1 = 47*53 + 249*(-10)
ANSWER: 47^-1 = 53 (mod 249)
here are some extremely delicate calculations for the inverse of 47 mod 249
normal thicket
Option was x=85mod249
onyx glen
,calc (53*11) mod 249
glossy valveBOT
Result:
85
yeah, that's correct.
normal thicket
Is there no other method?
onyx glen
trial and error
maybe some kind of sophisticated trial and error where you find the first multiple of 47 that is greater than 249, reduce that mod 249, then find the first multiple of THAT that overflows, reduce that, and so on.
i don't know how much faster that is.
may be equivalent to the euclidean algo in terms of effort
let me try actually, i want to see where this goes...
normal thicket
Yes. Please basically i was skipping Euclidean
onyx glen
slipping?
ok wait no that won't work my bad
my first step took me to 47 * 6 and that's already not good since 6 isn't coprime to 249
@normal thicket yeah sorry i don't know of any methods other than euclidean
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normal thicket
It took almost 30 minutes to learn
But it is nice way to solve
I want to learn x^2 mod
Please suggest which topic is that? Quadratic remainder?
@onyx glen
onyx glen
¯_(ツ)_/¯
normal thicket
How will you use Euclidean of
18x=60 mod 66
Gcd is not 1
One idea is that we divide it by 6
But when i use Euclidean it gives remainder 0😪
3x=10mod 11
We can't move 3 right side
Ohh i got it 7
18x=60 mod 66 when x=7
Thank you Ann
.close
normal thicket
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normal thicket
how did this happen?
warm abyss
how did this happen?
Are you unsure about why p can be 2 or why p^2 has to be 1 Mod 4 (except for p = 2)
Or do you have a problem with another one of these
normal thicket
I didn't actually understand what we were doing here
When we start from prime numbers p=2
normal thicket
0^2+1=1mod4
1^1+1=2mod4
2^2+1=1mod4
3^2+1=2mod4
I didn't understand the symbol in the option two lines and three lines
onyx glen
two lines is just the equals sign
it is impossible that you don't know that
three lines is modular congruence.
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abstract willow
Hello can i get help
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Hello can i get help
What step are you on?
1. I don't know where to begin
2. I have begun but got stuck midway
3. I got an answer but I'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above
@full forum 1.I don't know where to begin
<@&286206848099549185>
hello
hows your day going
im just dont know where to begin with this problem
I was wondering if you could teach me how to do it step by step
severe coral
<@&286206848099549185>
I would start by graphing y=sqrt(x+1) and then drawing the rectangles that are implied by the summation (1 is the width and height is sqrt(x+3/2)). From that you can figure out whether they are left-handed, right-handed, or midpoint
severe coral
Yeah, the height is from the summation
abstract willow
and so wiould i solve the summation notation with each x value or what
so (-1 plus 3/2) + (0+3/2) + (1 +3/2) + (2+3/2)
severe coral
yeah from x=-1 to x=2 you would get 4 terms, so you'd draw one rectangle with x=-1 and sqrt(1/2), the next one with x=0 and sqrt(3/2), etc. For 4 rectangles total
Yeah what you put would be the total estimate for the area
abstract willow
Hold on Im typing the graph into my calculator sorry for the delay
severe coral
no worries
severe coral
I got that it's midpoint. The first rectangle with x=-1 has height sqrt(1/2), so it should hit given parabola sqrt(x+1) at x=-1/2
abstract willow
oh i forgot the sq root
sorry hold on
could you show me how you do it on microsoft paint
because im still allite lost
@severe coral
severe coral
give me a minute, i did this on a whiteboard and will take a pic
abstract willow
ok thank you
severe coral
This is what I did, not quite drawn perfectly but the rectangles should intersect the parabola at the halfway points basically
abstract willow
Ohhhhhhhhhhhhh that how
ok and so how could i tell if it is a under or over estimate
severe coral
The only way I can think of is to actually integrate the function from -1 to 3 and compare it with the result of the summation. I can't really tell from the graph
abstract willow
I also have two more practice problems that my teacher sent us i was wondering if you could help with thoose two
too if you havethe time
severe coral
yeah sure
severe coral
working on it
severe coral
thanks i really apprecatte this
For #2, I'll say that if the interval is [-1,3] and we're using a right-hand riemann sum, the x-values we should use for each rectangle are 0, 1, 2, and 3 (and a left-hand would've been -1, 0, 1, 2). We can use that to figure out what the bounds of our summation should be and throw out 3 of the possible answers immediately
abstract willow
and you got that from drawing the graph correct
or should i automaticly make a refereance that right riemann sum does not start on the first number of the intervals
severe coral
Seeing the graph can be helpful, but you don't actually need it. They're giving nice numbers, they're asking for 4 equal rectangles and the interval [-1,3] is length 4, so the dividing points will be round numbers like that.
And yes, the right riemann sum never starts with the first number on intervals, left always does but never goes to the end
severe coral
Yep! And you would need to manually calculate each summation to figure it out between them
abstract willow
so i would plug in (Sqr root of 0+1) to Sqe root (3^3+1)
severe coral
yes
abstract willow
and for number 3 how about that one
severe coral
I thought I had it figured out but I think I messed it up, let me make sure I'm right, one sec
abstract willow
ok
severe coral
Ok so when dividing up [0,3] into three rectangles, one rectangle goes from 0 to 1, the next from 1 to 2, then the next from 2 to 3. They're all width 1
The height is going to be half-way between each interval because it's a midpoint riemann sum, so the height of the one from 0 to 1 is f(1/2), so you'd need to plug 1/2 into the original function to get its height
abstract willow
and so i would do f(1/2) plus f(3/2) plus f(5/2)
severe coral
yeah that's basically all it comes down to
abstract willow
sorry I pulled up one problem that my friend is haveing trouble with if its fine with you
can i pull he is in the room with me now
if you have time is all
severe coral
is it a problem like those? i dont have too much more time but can do a short one
abstract willow
its a short one i belive
severe coral
yeah i can take a look
abstract willow
severe coral
This one is kinda weird. You can treat it like your function is x^2+1 and your interval is [0,2], but I'm not sure how many rectangles you should make. Maybe try it with 2 rectangles to make it easy and calculate the left and right sums. For a parabola facing up like this, the left should be underestimating and the right overestimating. One of those intervals should hopefully contain the two results you get
severe coral
They might also mean one big rectangle but I'm really not sure. Hope it helps at least a little though
You too!
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abstract willow
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torn jolt
What is this question even saying
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What is this question even saying
torn jolt
?
rapid rain
the exact moment the ball is let go, it has a height of 2.11m and shot at an angle of 34.1°
basically this is oversimplified but suppose the only acceleration comes when the putter extends his arm
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ocean swallow
"Compounded continously, the amount of money in your bank account went from $1000 to $1051.28 in 5 years. How umch money will be in your bank account after 10 years if this trend continues?"
ocean swallow
okay i just have 1 question
is it saying 10 years AFTER the 5 years
or 10 years including those 5
light sonnet
is it saying 10 years AFTER the 5 years
I would say this
Because it says "if this trend continues"
So it's a continuation
tacit rapids
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tacit rapids
So i was taught that
You need to rationalize
Whenever you have roots on the
Umm
Denominator
So i think that photomath answer can be further simplifized?
Fied?
Am i right?
Like, shouldn’t you multiply both denom and numer with root(x)?
So that you rationalize
warm flicker
I mean technically
stiff musk
You need to rationalize
this seems to be a weird requirement by some schoolteachers.. i don't think most of the rest of us would consider sqrt(x)/x to be more simplified than 1/sqrt(x)
light sonnet
You need to rationalize
You don't need to, it's taught just cause it's a convention
wide sundial
Usually rearranging and simplifying is for the sole purpose of what you will do next to it
And learning to “simplify” is just learning to reorder your expression into something (possibly) more manageable
You will want different forms of your expression depending on the context
tacit rapids
Oh.. I see
I guess it depends on the teacher and how they want the answer but i see what you mean they both seem acceptable to me
Anyways thanks guys
Helped a lot
.close
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stiff swan
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stiff swan
My question is the last one
the last sentence
What's the difference if it doesn't have the origin
if it's still closed
split swift
what is F here?
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split swift
F isn't well-defined at zero because rho becomes zero
so the divergence integral isn't well defined if the surface encloses the origin, so gauss' theorem doesn't apply
if it doesn't enclose the origin, the divergence integral does make sense, so you can apply gauss' law
part a) is quite telling
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wary vine
A silly question
a circle is all the points which are equal distance from a single point (center of that circle)
an ellipse is all the points whose sum of distance from 2 points (ellipse's focal points) are equal.
does this pattern continue for 3, 4, 5.... n points? and generally, knowing "n", what all can we state about the nature if the shape made?
wary vine
ig ill just try drawing these shapes using pins and strings....
ashen crater
It's a cool question, but afaik there's no special name for them.. you can play around on desmos instead of pins and strings though (or maybe that's what you meant) but with even just 3 they can look pretty irregular
wary vine
oh!
thanks for reply bro..... (ha ha i finally got an unnamed thing in maths, an opportunity to engrave my name in history)
.close
swift fulcrum
Can someone help me with these problems?
I think a) is false since the x can have positive values
and I think b) is true because both can contain negative values
and lastly, I think c) is false because the absolute makes the function to contain negative values
Are my assumptions correct?
proper hawk
,w graph log_9(x^4)
glossy valveBOT
proper hawk
,w graph 4log_9(x)
glossy valveBOT
narrow helm
your reasoning seems correct except the first
proper hawk
,w graph 4log_9(|x|)
glossy valveBOT
swift fulcrum
That's just giving off the answers
narrow helm
yeah tbh
narrow helm
I think a) is false since the x can have positive values
wdym positive
narrow helm
do you mean negative?
swift fulcrum
your reasoning seems correct except the first
Only a)?
proper hawk
all i can do is show
swift fulcrum
I didn't ask for it though, did I?
narrow helm
everything else seems correct
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narrow helm
@swift fulcrum dont delete the original message, just type .close
this locks the channel for some time.
onyx glen
why not
swift fulcrum
My computer said so
swift fulcrum
That was a joke, and I just didn't want people to know who I am irl
Since some people I know have access to the same questions I have
onyx glen
are they that doxxable hm
swift fulcrum
Never bad to be safe
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timid nest
im having issues with this derivative, the result i got doesnt look like any of the answers ;-;
torn jolt
Show Ur work
swift fulcrum
im having issues with this derivative, the result i got doesnt look like any of ...
What's that è at the end of log?
wintry citrus
u forgot logx
timid nest
oh my god
shrewd hamlet
I woulda just done logarithmic differentiation
onyx inlet
im having issues with this derivative, the result i got doesnt look like any of ...
Is that e part of the question?
onyx inlet
Why does it have a leaf on top
cloud shore
Is that e part of the question?
it's part of the language my guy
timid nest
noo its part of the question in italian
onyx inlet
Oh I was confused
timid nest
it's supposed to be "the derivative of f(x) is"
swift fulcrum
I wanna learn Italian
timid nest
I wanna learn Italian
its cool but also pretty hard even for native speakers x_x
timid nest
im gonna free the channel so people with actual questions can use it :')
swift fulcrum
👍
timid nest
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wooden bolt
i dont really understand how they took the function inside the absolute value out and made it negative based on the fact that the function inside is negative
wooden bolt
if the overall value of something inside | | is negative, doesnt it still become positive when you get rid of the | |?
swift fulcrum
What a handwriting
swift fulcrum
if the overall value of something inside | | is negative, doesnt it still become...
It does
narrow helm
is g(k) negative?
wooden bolt
g(k) is any quadratic
its also the local minimum of h(x) when x=k
im just unsure how they went from line 2 to line 3 and 4
wooden bolt
oh i see
glossy valveBOT
narrow helm
if you take g(k) positive, then f(0) is zero
wooden bolt
so they just "got rid of" the | | by using the definition of |x|?
narrow helm
but ig the question has already given the value of f(0)
wooden bolt
if you take g(k) positive, then f(0) is zero
yeah but that doesnt work so they only consider the other case
narrow helm
so they just "got rid of" the | | by using the definition of |x|?
yes
wooden bolt
but ig the question has already given the value of f(0)
yeah f(x) is given
i see i see
thanks a lot
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strange basalt
17th one
wise gate
how do i find the range is my question here
Try to rewrite f(x) so it looks more simple
strange basalt
as in?
wise gate
Use polynomial division, for example
strange basalt
try it and lmk how can i do the same ...
i can split numerator
should i use completing the square?
i dont know im confused
willow sedge
17th one
You can let f(x)=y
||Now since Discriminant of x^2-3x+4 is negative, it(the quadratic) is always positive.
So you can multiply both sides by x^2-3x+4. Now note that discriminant of the quadratic in x would again be positive. This would give you a range of y values||
strange basalt
oh solve for x in terms of y?
right so i was getting something like this
got the range of y
willow sedge
This symbol should be negative
willow sedge
well, are you sure?
willow sedge
Yes
strange basalt
and integer sum would be -4-3-2-1 +0+1
strange basalt
wont i include it-
wait
oh its 3 . something smh
mb
my mind treated it like 4.something
willow sedge
Yeah it happens
strange basalt
got it
willow sedge
just like me forgetting 36 is not divisible by 13
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strange basalt
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narrow helm
shift - 2 to LHS
so the quadratic formed is > 0 and has leading coefficient positive
so D < 0
strange basalt
so D < 0
i was not able to diagonose this why is that true?
how did you determine d <0
strange basalt
the parabola is > 0
how did you determine that the parabola is >0
can you like share general forms
narrow helm
the inequality shows it
strange basalt
i cant recall them
narrow helm
i didnt determine anything
strange basalt
oh >0
narrow helm
you took -2 to LHS?
strange basalt
oh the inequality
narrow helm
yeah
cursive shuttle
You randomly pick 13 cards from 52 card deck. What are the chances that there are red, and black cards in your set?
Is my solution correct?
zenith kernel
No
cursive shuttle
how should I get the numerator then?
zenith kernel
You didn’t think about situations of black cards
sand stone
why not consider the chance of only red or only black
zenith kernel
Yeah
sand stone
it would simplify the problem a great deal
zenith kernel
-choose 13 from 26 blacks- choose 13 from 26 reds
cursive shuttle
why not consider the chance of only red or only black
i have more similar exercises to this that cannot be simplified this way
so i wanna know the rule
or way of solving it
zenith kernel
He just told you it can and I gave you the number
52C13-26C13-26C13
Is the number of cases your set has both red and black
sand stone
i have more similar exercises to this that cannot be simplified this way
it really just depends on the question
you have to read, understand and reduce
deduce*
cursive shuttle
thanks
sand stone
here we want the chance there is red and black cards
but there's lots.of ways to have both red and black cards
however we can look at it this way
what is the chance not having only black cards or only red carfs
cursive shuttle
1-chance of having both
sand stone
because those are the only two possibilities where we don't have both red and black
sand stone
1-chance of having both
exactly
cursive shuttle
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normal thicket
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normal thicket
So here infinitely solutions
here determinants will be zero when a=-3
What can I choose for lembda and u
I guess for all numbers where L+U =0
split swift
that looks good; if you want infinitely many solutions in 2d, the lines have to be the same, so L=-U as you say
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@normal thicket Has your question been resolved?
normal thicket
What if it is in 3d
I asked the same type question yesterday
When determinant is zero
I guess there are 2 possibilities
No solution and infinite solutions
split swift
there are a few ways to have infinitely many solutions in 3d
the planes could coincide, giving an infinite plane of solutions, or the three planes could form a sheaf, and we have an infinite line of solutions
split swift
if the some of the planes in 3d are parallel and not the same, or meet in a prism
then there are no solutions
normal thicket
Yes how will i solve the question
split swift
what question
tulip marlin
The determinant of what.
normal thicket
tulip marlin
the augmented matrix???
normal thicket
I got l =-2 then no solution
But i am feeling why
We can have no solution and many solutions no?
tulip marlin
i dont see how the determinant is immediately relevant, although it can be
normal thicket
@split swift
normal thicket
Nope
tulip marlin
then I dont understand.
normal thicket
Problem arises when 3d
normal thicket
How will you solve this
tulip marlin
row reduction.
split swift
yeah, you can solve it by setting the determinant of the matrix containing the coefficients to zero
but zero determinant doesn't guarantee no solutions
you still need to show that the system is inconsistent afterwards
(but given that the question says that setting this coefficient gives no solutions, I wouldn't bother)
basically, zero determinant is a necessary but not sufficient condition for inconsistency
normally, you'd have to do more work even after finding the coefficient that makes the determinant zero
but the way the question is phrased, you wouldn't in this case
split swift
I don't have any I can think of, let me look for a minute
8:11 into the second video discusses inconsistent systems
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@normal thicket Has your question been resolved?
green trail
question
green trail
swift fulcrum
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1. I don't know where to begin
2. I have begun but got stuck midway
3. I got an answer but I'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above
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Show your work, and if possible, explain where you are stuck.
green trail
I'm typing dude
Ok so I square root (9-3)^2
9 - 3 = 0
Would that not be 9 - 3 = plus minus 0
swift fulcrum
Yes
green trail
but it doesn't matter cuz its zero?
swift fulcrum
But you don't need to root both sides here
green trail
why
swift fulcrum
but it doesn't matter cuz its zero?
And yes
It's just numerical calculations
PEDMAS
Oh sorry
That's a q, not a 9
Shouldn't made sense anyways
green trail
right mb
swift fulcrum
but it doesn't matter cuz its zero?
Regardless this is the answer you're looking for
green trail
gotcha
so if it was 6 on the other side
it would be q - 3 = plus minus 6? ?
how would you continue solving for q
is it q = plus minus 9
weird
pale dome
not quite, for future reference im going to use "pm" for "plus minus"
we have q-3= pm 6 correct?
lets break up the equation into separate cases, where 6 is negative, or 6 is positive
that will get us
q-3=-6
and
q-3=6
following so far?
green trail
huh I see
pale dome
yep
green trail
real quick whats the latex for pm
pale dome
now lets solve the next equation (q-3=6)
pale dome
real quick whats the latex for pm
i dont know tbh i can prob find it somewhere
green trail
now lets solve the next equation (q-3=6)
would be q = 9
pale dome
great job, so q= 9 and -3
green trail
turns out its just \pm
pale dome
yeah i just searched it and was gonna tell you lol
green trail
about this
why do we never care about the coeffficent 2
why is it just the binomials ?
oh cuz they have the variables
?
pale dome
we are to set each factor equal to 0, but since the factor 2 cannot equal 0 no matter what we do, we do not care about the 2
green trail
gotcha
so not exactly cuz its variable
but also exactly bc of that?
bc with variables there is a possibility of a zero
pale dome
well you can have a factor that has variables and still disregard it
green trail
can you show an example
pale dome
for example if we have (x^2+1)(x-2), we can disreguad the factor (x^2+1) because it will not equal 0
thus we only need to set the factor (x-2) equal to 0
(unless were solving for complex roots too)
pale dome
if your not learning complex numbers then please disregard that, i was just adding that to be accurate
green trail
How would you solve for complex number there
Can you just show the steps no explanation
split swift
\begin{align*}
x^2+1&=0\
x^2&=-1\
x&=\pm i
\end{align*}
glossy valveBOT
Desync
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@green trail Has your question been resolved?
pale dome
square-rooting it right off the bat wont lead anywhere
instead, try to isolate w^2 then square root it
green trail
so it's always necessary to factor first
pale dome
i mean we can factor here but there is another method
green trail
Do I have to take out the gcf 2 or can I do something else?
pale dome
are we factoring to solve or are we using the square root function to solve?
green trail
factoring would just lead to the scenario above right?
pale dome
yes
green trail
Ok let's square root
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pale dome
instead, try to isolate w^2 **then** square root it
ok then, first do what i suggest here ^
pale dome
not quite, were aiming to have w^2 alone correct?
green trail
sqrt other side
green trail
not quite, were aiming to have w^2 alone correct?
ok so just divide 2
green trail
Got it! Thanks.
pale dome
np :D
green trail
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rose dust
How can I traduce this:
x - 1 & \text{si } x \geq 0 \
-x - 1 & \text{si } x < 0
\end{cases}
spice orchid
. @split swift behold trade helper secrets
small maple
My answer is wrong. Can’t say much else.
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My answer is wrong. Can’t say much else.
@small maple Has your question been resolved?
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onyx inlet
How old are you brother
onyx glen
but also yeah, how old are you
we only ask because we need to know if you're under or over 13. you're fine.
khanacademy has good resources for basic math like that.
might want to ensure you know addition and subtraction well before going on to multiplication.
can you reliably add/subtract numbers of three digits or shorter, let's say
w/o messing up or second-guessing yourself
onyx inlet
How are you straight A in Physics and Chemistry at 16
And you don’t know multiplication?
Oh
How does one not have the ability to multiply
weak iron
...
onyx glen
@onyx inlet this line of questioning will go nowhere. cease at once.
OP already said not to ask him.
in that case, get yourself more practice in addition and subtraction.
until you are 100% confident w/ those.
surreal hull
I am trying to solve the following problem:
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I am trying to solve the following problem:
surreal hull
I came up with the following solution, could someone check if my logic makes sense?
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@surreal hull Has your question been resolved?
onyx glen
this feels inelegant. why use contradiction at all?
surreal hull
is there some way to choose epsilon without assuming such a c exists?
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@surreal hull Has your question been resolved?
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@surreal hull Has your question been resolved?
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@surreal hull Has your question been resolved?
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@surreal hull Has your question been resolved?
surreal hull
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