Available help channel!
#help-28
full forumBOT
Available help channel!
drifting dune
why is there a ± in front of a square root like in the quadratic equation
but when there is a limit there is no ± in front of the square root!!!!
WHY
barren needle
the square root is defined as positive?
nova basin
why would you expect a +- to be there ? That's just a random limit, it doesn't stem from the quadratic equation
nova basin
it's not a quadratic equation
why are you bringing the quadratic formula to this innocent, simple limit ?
limber flicker
I would say when you are solving for a variable that is satisfied by +- x then you have the pm sqrt
as you solve for when x = -b + blah blah blah
jovial wing
why is there a ± in front of a square root like in the quadratic equation
but ...
that's completely unrelated
limber flicker
^^
tall juniper
In the middle of the derivation of the quadratic formula we have
(x+b/2a)² = (b²-4ac)/4a²
And when we root both sides we get
x+b/2a = ± √(b²-4ac)/√(4a²)
x+b/2a = ± √(b²-4ac)/2a
jovial wing
if x is on the other side
tall juniper
But in the limit nobody rooted both sides, it was just given as is
hallow walrus
$x^2=a\implies x = \pm\sqrt{a}$, but $x=a\nRightarrow \sqrt{x}=\pm\sqrt{a}$
glossy valveBOT
kheerii
drifting dune
hmmm
tall juniper
**kheerii**
I mean if you have x=a you wouldn't root both sides because you're trying to solve for x, right?
hallow walrus
it was just an example of when the plus minus appears and when it doesnt
drifting dune
.close
dark seal
hello, I have this exercice for practicing distance vectors:
it asks for me the point or points at the straight that are at two of distance from P(-2,2)
this is what the exercice tells me: r: (x - 1) / 2 = (y + 1) / -1, that the distance between the point P and the other points must be 2 (d = 2) and that the point P is P(-2,2)
What I though is to use the formula d = |Ax1 + By1 + C| / sqrt(a^2 + b^2), so first I got the general equation: x + 2y + 1 = 0, moreover, A = 1, B = 2, C = 1
(in what I was trying I supposed there is just 1 point at the line, but I don't know if it is good) the point that is in the line I called it O and then the width betweeen O and P is 2, so | OP | = 2, | OP | = P - O = (Px, Py) - (Ox, Py) = (-2,2) - (Ox, Oy) (this I am not pretty sure if it is right)
and I think aswell that | OP | = sqrt((Px2 - Ox1)^2 + (Py2 - Oy1)^2)
and then I am stucked here, because I don't know how to find the x1 and y1 from the formula distance between a point and a line, should I not use this formula?
how could I continue?
full forumBOT
hello, I have this exercice for practicing distance vectors:
it asks for me the ...
@dark seal Has your question been resolved?
full forumBOT
@dark seal Has your question been resolved?
upbeat relic
Problem 2....
I see we have to use contradiction to prove it mathematically,but I am not getting it why suppose (0,1/3) or (0,1/5) is not included(subset ) of (0,1) or (0,1/2) and similar for others !??!?
ember shadow
,rccw
glossy valveBOT
ember shadow
what specifically is your question? do you know how to form that intersection?
upbeat relic
As far as i know intersection is the common part of 2 or more sets ,
Now when we are taking n=1,its suppose A1= (0,1)
When n=2
ItsA2= (0,1/2) and so on .
My question why in this case Intersection (0,1/n)
A1's subset A2's subset A3 ...... and so on
Then it wouldn't be null obviously .
ember shadow
A1 is not subset of A2
ember shadow
right
nova basin
take the intersection up to a given N. that should help you understand
ember shadow
so what is $A_1 \cap A_2$
glossy valveBOT
cwatson
upbeat relic
No tell me one thing for example intersection of (0,1) and (0,1/3) is null
But isn't (0,1/3) a subset of (0,1)?
nova basin
" intersection of (0,1) and (0,1/3) is null " no it's (0, 1/3)
upbeat relic
take the intersection up to a given N. that should help you understand
Oooooo i seee... when we are taking infinity ,we are getting into trouble ....🤦
ember shadow
what "trouble"?
nova basin
take the intersection up to a given N. that should help you understand
that's why I said this
upbeat relic
that's why I said this
Genius....🙇
Then it is becoming (0,0) hence null ....., I guess .
Not trouble,but the explanation
Thanks for your time ..... Sir ✅
@ember shadow @nova basin
full forumBOT
@upbeat relic Has your question been resolved?
spark sundial
how would i find the confidence interval for this question?? im not quite sure I'm doing the process right (I have a ti-84 calculator I'm using)
i got this question wrong on a test, so don't mind my previous answers and instead look at the second image attached for my process
spark sundial
please @ me if anyone responds 🙂
full forumBOT
@spark sundial Has your question been resolved?
spark sundial
<@&286206848099549185>
full forumBOT
@spark sundial Has your question been resolved?
full forumBOT
@spark sundial Has your question been resolved?
spark sundial
.close
median beacon
full forumBOT
median beacon
because AT prime is diagonal
does that mean that the vectors in the basis B prime are eigen vectors?
according to this
fast peak
yes
median beacon
yes
here it says the eigenvectors are the standard ordered basis
shouldnt it be B prime
fast peak
well not of that matrix....
median beacon
thats what i initally asked tho
fast peak
they are eigenvector of A_T
median beacon
oh ok
median beacon
they are eigenvector of A_T
that doesnt make sense tho
according to the prop it says the eigenvectors of the basis B in relation to AT
not AT prime
fast peak
the prop is using different notation
in their notation A_T would be T and A_T prime would be A_T
median beacon
in their notation A_T would be T and A_T prime would be A_T
u mean A_T would be A_T prime and A_T prime would be A_T?
fast peak
I meant what I said
full forumBOT
Available help channel!
spring wedge
what exactly is the simplest form of a number?
so like for a number like 4, is 2+2 simpler than 4? or is it 1 + 1 + 1 + 1?
spring wedge
recently i asked what was simpler, sqrt(68) or 2sqrt(17) and it was the latter because the number inside of the square root was smaller, i was wondering if this applies with all simplification related stuff, just the smallest version of the thing you're trying to simplify but it's also equivalent
civic basin
4 is the simplest form of 4
cause its integer
sqrt(68) exact value would be in decimal form, so for it to be in the simplest form, you need to write it as smallest number in sqrt as it can be
and factor out the integer
like sqrt(4*17) = 2sqrt(17)
spring wedge
so if it's not a perfect square root, you have to make the number inside of the square root as small as possible?
civic basin
yes
spring wedge
but wouldn't the exact value of 2sqrt(17) also be a decimal?
civic basin
yes, it would be almost exact value as sqrt(68)
light sonnet
but wouldn't the exact value of 2sqrt(17) also be a decimal?
Irrational numbers aren't exact
spring wedge
yes, it would be almost exact value as sqrt(68)
So why is 2sqrt(17) simpler?
light sonnet
You want to simplify the inside as much as possible
civic basin
So why is 2sqrt(17) simpler?
because 2 as integer have more precise value than any sqrt
alone
spring wedge
You want to simplify the inside as much as possible
i get that, but why does it make it simpler?
spring wedge
because 2 as integer have more precise value than any sqrt
so, 2sqrt(17) is more precise than sqrt(68)?
civic basin
let me know, whats simpler to you?
I will be 10 years old in 34 months.
or
I will be 10 years old in 2 years and 10 months.
light sonnet
so, 2sqrt(17) is more precise than sqrt(68)?
Do you know the concept of adding/subtracting radicals?
spring wedge
let me know, whats simpler to you?
I will be 10 years old in 34 months.
or
I wi...
the latter
spring wedge
Do you know the concept of adding/subtracting radicals?
nah, it's not required for our syllabus
but i've just been doing math on my own to learn about it and i came across this which i don't really understand
light sonnet
Because take $\sqrt{108} + \sqrt{12}$, first glance, you'd assume that you can't add them because the number under isn't the same but if you simplify it, $\sqrt{108} = 6\sqrt{3}$ and $\sqrt{12} = 3\sqrt{3}$, you'll notice that you can add them
glossy valveBOT
dldh06
civic basin
the latter
then, you answered yourself, imagine that sqrt are months, and years are integers
spring wedge
i see
spring wedge
then, you answered yourself, imagine that sqrt are months, and years are integer...
so it's because mathematically 2sqrt(17) is easier to understand over sqrt(68)?
civic basin
and you can do a lot of more things with 2sqrt(17) than sqrt(68)
spring wedge
alright
hoary hound
full forumBOT
silk rock
is this correct?
full forumBOT
is this correct?
empty sapphire
yeah seems right to me
full forumBOT
@silk rock Has your question been resolved?
silk rock
yeah seems right to me
And then its domain is:
Dom(g o g) = [-5, 0)
empty sapphire
oh wait no. The domain should be the same
.... I think
you only need to restrict the domain if need be. Like if you had a rational or square root function
things like that
but you're passing all real numbers into all real numbers, so you're good fam
silk rock
you only need to restrict the domain if need be. Like if you had a rational or s...
I thought that the Domain of a segmented function was a disjunction of its conditionals
silk rock
I'm confused about the domain of a composed function:
Dom(f o g) = {x∈Dom(g) / g(x)∈Dom(f)}
full forumBOT
full forumBOT
Available help channel!
dim compass
R={(x,y)|x and y are real numbers and x=wy for some rational number w}
dim compass
I want to know if the relation is reflexive or not
The tricky real number that seems problematic is 0
fast peak
well is x=wx for some rational number w?
dim compass
well is x=wx for some rational number w?
Yes
I don't know if I should take w to be rational number for granted or not
fast peak
well for which rational number does it hold
dim compass
well for which rational number does it hold
x=wy?
fast peak
x=wx
dim compass
If any rational number other than w=1 is there
it doesn't follow x=wx
So should it be non reflexive?
fast peak
"for some rational number" means "at least one"
fast peak
for x=0 there would be others but for nonzero x there is only w=1
dim compass
for x=0 there would be others but for nonzero x there is only w=1
For x=0 w can be irrational
Does that not disobey the question
That w should be some rational?
dim compass
In question x can be any real number, so it can be 0 and when it is 0, w=irrational worms
dim compass
it holds for some rational
That seems kind of contradictory
In question it says it hold for some rational number w
But when we analyse the question it can work for non rational number w as well when x=0
But you're right from your perspective
.close
full forumBOT
full forumBOT
Available help channel!
vale karma
Can anyone help me solving this exercise about complex number, the answer is on the right
wary walrus
try using the fact that x is a real number if and only if x is its own conjugate
full forumBOT
@vale karma Has your question been resolved?
vale karma
try using the fact that x is a real number if and only if x is its own conjugate
how can I write what you said?
wary walrus
$z \in \mathbb R , \Leftrightarrow , z = \overline z$
glossy valveBOT
Gio'
vale karma
But, how can this affirmattion help me?
wary walrus
you want (conjugate of z) * (z^2 - 1) to be real
wary walrus
I guess so because the answer uses this form
vale karma
but, do I have to do the operations including the i or not?
wary walrus
what do you mean by that ?
wary walrus
I think so
vale karma
i did it but it has no sense because it's an enormous expression
dark cobalt
for i) isnt the answer just 0.9? not sure why we need to calculate anything
dark cobalt
with P(E) being forgot to submit and
P(H1) = finished work
P(H2) = did not finish
and for ii) have I done this right?
$P(H_1 | E) = \frac{0.01 \cdot 0.9}{0.01 \cdot 0.9 + 0.5 \cdot 0.1 }$
glossy valveBOT
yotta
dark cobalt
<@&286206848099549185>
thin flint
90% or 0.9 is the number of students that finish their assignment on time as a percentage of the total, not the number of students that forgot to submit their assignment
full forumBOT
@dark cobalt Has your question been resolved?
dark cobalt
90% or 0.9 is the number of students that finish their assignment on time as a p...
wait so
are you saying H1 and H2 should be forgot to submit and didnt forget to submit?
or
the answer to part i should be 0.01 * 0.9 + 0.5 * 0.1
?
@thin flint
thin flint
i'm saying that the prior probability that a student forgets to submit their assignment is different
it requires a bit of calculation
dark cobalt
it requires a bit of calculation
what would we do
thin flint
0,9 completes on time
so 0,1 doesn;t
of those who complete on time 1/100 doesn't submit
forgets
and half of those who don't complete on time claim to have forgottem
forgotten
thin flint
that is the answer to i
dark cobalt
**yotta**
so would this be right
for ii)
since it wants
finished | they forgot
? @thin flint
full forumBOT
@dark cobalt Has your question been resolved?
dark cobalt
oh nw :p
full forumBOT
@dark cobalt Has your question been resolved?
full forumBOT
https://gyazo.com/524e0c73e8a6e95204a2023fcc60ea9a
torn jolt
So I have two planes here, the rainbow one is pythagorean theorem z=sqrt(x^2+y^2) and the blue one is a linear approximation I made. The blue graph matches the rainbow colored one in y=x, however the further away from the line y=x the more discrepancy there is between the blue and rainbow one. How could I transform the blue graph so it matches the rainbow one better.
Because it is for a specific engineering project its important to keep x and y seperated, so no x*y or sqrt(x y) or anything like that.
Also, blue and rainbow dont have to match exactly, I just need a pointer in the right direction how I can 'curl' the blue graph a bit
white geyser
if a linear approximation curves its not linear anymore.
torn jolt
if a linear approximation curves its not linear anymore.
My apologies for the confusion, it does not need to be linear. Only x and y need to be kept seperated.
<@&286206848099549185>
woeful hatch
hm
woeful hatch
<@&286206848099549185>
is this positive x and y only?
woeful hatch
right
let me just figure out how to restrict geogebra 3d input in x and y
ok here's my illustration of the equations
that red thing is the y = x plane
what did you put in to make your blue plane?
torn jolt
approximately z = 0.5 * (0.96043x+0.39782y+0.96043y+0.39782x) x c
adjusted c a bit so it adds up nicely over y=x
woeful hatch
right
torn jolt
approximately 1.03, cant find the whole variable
Its a formula I derived from this algorithm, if its of any help
woeful hatch
ah, is that why the x and y are split into 2 parts?
and yes that does help
are these where your x and y come from?
torn jolt
yes, basically did it 2 times adding it to eachother
divided by 2
to eliminate the min max thing
but now the <4% deviation is lost
woeful hatch
my instinct would be to split it into two planes: one for x < y, and one for x >= y.
to simulate how the curve bends around the z-axis
not sure about how to curl (as you put it) the graph
torn jolt
Mm, how would I do that?
for the project I really need it as one formula, that would be able to be split into 2
woeful hatch
hold on
partial derivatives might help
what are $\frac{\partial z}{\partial x}$ and $\frac{\partial z}{\partial y}$?
glossy valveBOT
OutOfNosh
woeful hatch
so it's $\frac{x}{\sqrt{x^2 + y^2}}$, which rules out that idea, since you're not allowed to mix x and y
glossy valveBOT
OutOfNosh
woeful hatch
idk
torn jolt
I got a new idea, but I will try it tomorrow as its late here
woeful hatch
for the project I really need it as one formula, that would be able to be split ...
would they let you build it as a case?
torn jolt
would they let you build it as a case?
What do you mean?
woeful hatch
i.e. if x >= y, have the formula spit this out, otherwise, spit that out?
torn jolt
That would not be possible, because the inputs are mechanical
woeful hatch
but still present it as one formula?
torn jolt
things would get too complicated unfortunately
the idea was, z = f(x) + g(y)
so it needs to be ablle to 'split' like that
full forumBOT
@torn jolt Has your question been resolved?
full forumBOT
full forumBOT
Available help channel!
rancid salmon
Can someone help me solve the question below the scatter plot?
rancid salmon
<@&286206848099549185>
digital willow
rancid salmon
no
im not sure if its correct
but is it correct?
oh alr
yea
idk why
yes
ok..
a lil
my teacher never taught us this. just gave it to us
yea
cuz of the lune of best fit
?
and the points basically touches the line?
oh
ok
shrewd hamlet
What’s the fastest way to do this?
full forumBOT
What’s the fastest way to do this?
shrewd hamlet
(Solve the system)
currently doing lagrange multipliers and not having a fun time doing these by hand
normal tree
have you tried using a computer algebra system lol
shrewd hamlet
ive searched up system of nonlinear equations solver and the one i tried didnt work
couldnt find any other decent ones
do u have a site u can recommend?
yea i tried symbolab but it didnt work unforuntately
ye, ill show u
hmm
alr imma try
did some more manual and tried to plug in, still didnt work
:/
wait how would i do the eigenvectors for the nonlinear part
.close
full forumBOT
full forumBOT
Available help channel!
slate ivy
full forumBOT
slate ivy
can some one tell me how did we get the red circled part
buoyant gust
can some one tell me how did we get the red circled part
(1 + dy/dx) was multiplied with 3(x+y)^2.
Like this:
a(b + c) = ab + dc
Where in this example a is 3(x+y)^2
buoyant gust
So the one became 3(x+y)^2.
And the dy/dx became 3(x+y)^2 dy/dx
So result is 3(x+y)^2 + 3(x+y)^2 dx/dy
You get it now?
slate ivy
yeah
buoyant gust
Alr
full forumBOT
buoyant gust
Np
full forumBOT
Available help channel!
dark violet
i need help with Equivalent fractions
full forumBOT
i need help with Equivalent fractions
dark violet
dark violet
yes
lapis gate
wym
dark violet
lapis gate
Ok well the easiest way in this case is to simplify each fraction as much as you can
Do you know how to simplify a fraction? Like what is the simplest way you can write 16/20?
dark violet
not really
lapis gate
So for 16/20 what is a number can go into both 16 and 20?
dark violet
10?
dark violet
no
lapis gate
ok so try a different number xD
dark violet
its really not that funny
lapis gate
? I'm helping you
dark violet
So for 16/20 what is a number can go into both 16 and 20?
2
lapis gate
exactly
So you can divide both 16 and 20 by 2 to get an example of an equal fraction
so 16/20 can also be written as 8/10
dark violet
ok
lapis gate
Now how can you reduce 8/10 even more? Is there a number that goes into both?
dark violet
2
lapis gate
yep 😄 so 8/10 can also be written as 4/5
and now you can see there's no way that you can reduce it more
so that is the simplest way that you can write it
dark violet
kinda
lapis gate
Do you understand how we reduced 16/20 to get it to 4/5?
dark violet
2
lapis gate
No I know but you understood the process right?
dark violet
suree
lapis gate
Ok awesome
So now what you should do is do that for each of the answer options
and see which ones also reduce to 4/5
So for example, does 2/3 reduce to 4/5?
dark violet
no
dark violet
yes
lapis gate
What would you do to reduce it?
dark violet
4/5?
lapis gate
Yep you are right!
So you can see how then 16/20 also can equal 12/15?
because both of them are the same when they are reduced
dark violet
this is too confusing
dark violet
everthingg
lapis gate
Just remember
you need to reduce the fraction as small as you can
that is the first step
lapis gate
That's as small as you can go!
dark violet
oh
lapis gate
You can't reduce 3 or 5 by anything smaller right?
dark violet
wait
lapis gate
So that would be your simplified fraction
dark violet
let me send a screen shot
lapis gate
sure
dark violet
lapis gate
Ok so that one is already reduced right?
What about 12/20?
Can you reduce that one?
dark violet
no
lapis gate
Why not?
lapis gate
both work
dark violet
oh
lapis gate
so if you reduce it by 2 it would be 6/10 right?
now can you reduce 6/10 even smaller?
dark violet
yah
lapis gate
By 2 again right?
dark violet
yah
dark violet
yah
lapis gate
Now what about 9/15?
dark violet
by 3?
dark violet
no
dark violet
k
lapis gate
Do you understand how to answer the question now?
dark violet
yah wanna know somthing
lapis gate
sure
dark violet
i have answered 150 qustions 😭
lapis gate
Correctly? or wrong
dark violet
mostly wrong like 15 right
lapis gate
I think you can do more correct now though
You seem to understand it
Want to do one more together?
lapis gate
Ok first can you reduce that more?
dark violet
no
lapis gate
Are you sure?
dark violet
no
lapis gate
What can go into 2 and 16 evenly?
dark violet
2
dark violet
yep
full forumBOT
full forumBOT
Available help channel!
torn jolt
what are the quartiles to the box plot?
full forumBOT
what are the quartiles to the box plot?
terse karma
What does she say?
torn jolt
she says the box plot below shows the distribution of ages
terse karma
Did you find the quartiles
torn jolt
the box plot is incorrect, and I know the quartiles is wrong but i'm not sure what they are supposed to be
terse karma
You have to find Q1 ,median and Q3
terse karma
i'm asking how to find it
There are 10 numbers so you have to get the 10i/4 th number for i th quartile
Second quartile is equal to median itself so just find Q1 and Q3
torn jolt
i don't understand but ok 😭..
terse karma
i don't understand but ok 😭..
Well 10/4 = 2.5
Righr
So we get the mean of 2nd and 3rd number to get Q1
What's the 2nd and 3rd number?
torn jolt
why would i need the mean?
terse karma
why would i need the mean?
What do you do to find median when the number of entries are even?
Oh yes it's not required to find mean in here
It's 2.5 so the Q1 will be just 3rd number itself
torn jolt
.close
full forumBOT
full forumBOT
Available help channel!
wintry cosmos
do you know what a discriminant is?
remote tartan
glossy valveBOT
wintry cosmos
@torn jolt substitute and simplify...
vast fossil
Quadratic formula is lowkey an overkill though
wintry cosmos
a, b are the coefficients of x^2 and x respectively and c is the constant
vast fossil
We don't do that here
wintry cosmos
*ax^2
vast fossil
torn jolt
you say heres a formula but not saying wtf it is
vast fossil
Helping =/= Giving away the answers
torn jolt
how am i supposed to use a formula when idk what goes where
why can't you just google the formula for the discrimannt ? what's so hard about it
vast fossil
you say heres a formula but not saying wtf it is
They have explained it
glossy valveBOT
Stephen
torn jolt
"substitute and simplify"
vast fossil
So, you haven't been introduced to the quadratic formula yet?
wintry cosmos
Standard form → $ax^2 + bx + c \$
Discriminant → $b^2 - 4ac$
glossy valveBOT
torn jolt
probably a more instructive answer would be to ask him to figure out the determinant
I mean the discriminant
nvm i found a site that gives me answers
torn jolt
So, you haven't been introduced to the quadratic formula yet?
idk what that is
torn jolt
nvm i found a site that gives me answers
does the site solve poverty
no but it solves answers
So
solves answers... Hmmm
vast fossil
So do you want to get help here or not
And by 'help' I mean guidance through the problem
torn jolt
what does this mean
I thought the site gives you answers
but it doesnt give tell me how many there are
okay. Do you have some ideas
the discriminant is 32
-32
oops
but
ok
negative means none
so ?
vast fossil
Then it has two
wintry cosmos
torn jolt
but how do i know if it has one
wintry cosmos
this might help
torn jolt
im not using that formula-
vast fossil
but how do i know if it has one
That happens when the discriminant is 0
wintry cosmos
well, find the discriminant
vast fossil
2y^2 - 7y + 4 = 0 has no real solutions because its discriminant is negative
torn jolt
so you lied
the website lied
vast fossil
It's 0 solutions when D < 0
wintry cosmos
d < 0 is no real solutions
vast fossil
no one knows what d < 0 means
D is discriminant
wintry cosmos
where were we again?
wintry cosmos
is that IXL btw?
wintry cosmos
so $f(z)$ is a function and the output is $z^2 - 2z$
glossy valveBOT
wintry cosmos
input the given 'z' value into f(z) and you'll get the value
wintry cosmos
basically just substitute the given 'z' value into 'z^2 - 2z' and fill the table accordingly
torn jolt
do you think i can do 8 more of these ixls and finish today
torn jolt
oh
grave elm
Would the following be injective map from Q+ to N? I have positive fraction a/b where a and b are coprime, then I would just do a*b to map it to N. Would this be injective?
torn jolt
Would the following be injective map from Q+ to N? I have positive fraction a/b ...
prima facie it's possible to have an injection from Q to N
(I think)
grave elm
prima facie it's possible to have an injection from Q to N
2^a*3^b
this is what I found, I just wanted something simpler
torn jolt
prima facie it's possible to have an injection from Q to N
Q and N have the same cardinality, so in fact there is a bijection between them
torn jolt
Q and N have the same cardinality, so in fact there is a bijection between them
yeah that's right. I'm rusty
spiral latch
hii
spiral latch
i want to help for fix my question
30Z⁴ + 5Y³X⁵ - 3XZ
x = 2
y = 3
z = -4
my answer is 207.360.000
so I wanted to see if it's right
onyx glen
,w 30 * (-4)^4 + 5 * 3^3 * 2^5 - 3 * 2 * (-4)
glossy valveBOT
onyx glen
nope
torn jolt
so I wanted to see if it's right
use a calculator mate
spiral latch
i want to resolve to solve 30Z⁴ + 5Y³X⁵ - 3XZ
x = 2
y = 3
z = -4
rugged heron
you want to verify?
drifting dune
re solve
rugged heron
what does re solve mean in this context im a lil lost
drifting dune
he solved it wrong before
spiral latch
I did but I didn't get it right, and I'm not getting it right
So I wanted to help me solve it right
rugged heron
what do you have in mind to solve this?
spiral latch
1 minute
torn jolt
i want to resolve to solve 30Z⁴ + 5Y³X⁵ - 3XZ
x = 2
y = 3
z = -4
that's not what solve means
spiral latch
I'm Brazilian and I'm using the translator sorry
rugged heron
it is wrong i think
torn jolt
it is wrong i think
where is he wrong
rugged heron
this is what they are referring to i believe
spiral latch
you just replace x y z with their values what's the problem
the problem is when i get to 5y^3x^5
torn jolt
this is what they are referring to i believe
what's false about it
torn jolt
the problem is when i get to 5y^3x^5
yeah what about it
rugged heron
what's false about it
im just as lost as you rn bro lol
torn jolt
im just as lost as you rn bro lol
loool
spiral latch
what do you have in mind to solve this?
30 * (-4)^4 + 5 (3^3*2^5) - 3 (2 * ( -4)
30 . (-4)^4 + 5 (3^3.2^5) - 3 (2 . ( -4)
. is multiplication
after that i do
30 . 256 + 5 ( 27 . 32 ) - 3 ( 2 . ( -4)
is it correct so far?
vital shadow
yea
vital shadow
3*2*(-4) does not equal 6*12
spiral latch
- 72?
spiral latch
oh
spiral latch
30 . 256 + 5 ( 27 . 32 ) - 3 ( 2 . ( -4)
but when there's no signal like that, isn't it supposed to rain?
3 ( 2.(-4))
3.2
and
3.-4
spiral latch
what's 2*2
4
vital shadow
and 4*3?
spiral latch
12
vital shadow
you don't need to
spiral latch
why
vital shadow
what's 3*2
spiral latch
6
vital shadow
6*4?
spiral latch
-24
spiral latch
yes
in truth no
because
I think we should first multiply the 3 by the 2 numbers
then multiply them
vital shadow
ok nvm, ignore that
vital shadow
for now, just know that the picture you sent is incorrect
spiral latch
3 ( 2 * -4 )
3 * 2 3 * -4
6 - 12
vital shadow
yea
vital shadow
no
vital shadow
30 . 256 + 5 ( 27 . 32 ) - 3 ( 2 . ( -4)
5*27*32 does not equal to 135*160
u did the same thing here
vital shadow
yea
vital shadow
not quite, where does -94 come from
spiral latch
7680 + 21600 - 72 - 24
-72 -24
vital shadow
remember that we left out the negative when multiplying for the last term
so 12000 - (-24)
spiral latch
but there are no parentheses
spiral latch
-6 * -4
vital shadow
yea so +24
spiral latch
so 12000 - (-24)
- 24
vital shadow
at first, I left out the "-" in the -3 and just used 3 to multiply instead
im sorry for the confusion
atomic vortex
so I used partial fractions and got 1/4n - 1/(4(n+4)) but idk what to do from there
atomic vortex
I saw a vid and when the dude was doing it he was cancelling values as he was expanding the sum
but for me the pattern is something like
$\bigg(\frac{1}{4} - \frac{1}{20}\bigg) + \bigg(\frac{1}{8} - \frac{1}{24}\bigg) + \bigg(\frac{1}{12} - \frac{1}{28}\bigg) + \cdots$
glossy valveBOT
Calc II Victim
atomic vortex
n+4 means it should repeat every 4 terms
$\bigg(\frac{1}{4} - \frac{1}{20}\bigg) + \bigg(\frac{1}{8} - \frac{1}{24}\bigg) + \bigg(\frac{1}{12} - \frac{1}{28}\bigg) + \bigg(\frac{1}{16} - \frac{1}{32}\bigg) + \bigg(\frac{1}{20} - \frac{1}{36}\bigg) + \bigg(\frac{1}{24} - \frac{1}{40}\bigg) + \bigg(\frac{1}{28} - \frac{1}{44}\bigg) + \bigg(\frac{1}{32} - \frac{1}{48}\bigg) + \cdots$
glossy valveBOT
Calc II Victim
atomic vortex
so 1/28 did end up cancelling after 4 more
same with 1/32
and 1/24
but
what about
1/8 and 1/12
and 1/16
atomic vortex
so I will be left with 1/4 + 1/8 + 1/12 + 1/16
torn jolt
yea
atomic vortex
holy shit this is acc so cool
atomic vortex
n+4 means it should repeat every 4 terms
lets say I had something like 1/n+1 and 1/n+2
what would that mean
repeat every 3 terms?
like how can u just tell from looking at the denom
without drawing out the sum
torn jolt
like $\sum_n \frac1{n+1} -\frac1{n+2}$?
glossy valveBOT
Toby
atomic vortex
yep
torn jolt
it repeats every term
torn jolt
it repeats every term
**every one term
torn jolt
oh u j look at the second denom?
(n+2) - (n+1) = 1
atomic vortex
OHhhh
torn jolt
so I used partial fractions and got 1/4n - 1/(4(n+4)) but idk what to do from th...
4(n+4) - 4n = 4
torn jolt
yup 
atomic vortex
bro tysm
atomic vortex
.close
full forumBOT
Available help channel!
maiden pike
full forumBOT
maiden pike
im not sure where to start in this question
torn jolt
always start out with a diagram
so u got a diagram of the traingle right
isoscles has two equal sides
so it has two sides of 9x + 3
since the total Perimeter is 30x - 10
u can subtract 2* (9x+3)
so then u get the value of the base
30x - 18x -10 + 6
12x - 4 is the base
base to perimeter is 12x - 4 to 30x + 10
divide by 2 for obht sides to simplify the ratio
6x - 2 : 15x + 10
the restriction on x is is it must be +ve
because if it isn't postive u will get an a negtaive numberr
and thus a negative premeter which is impossible
@maiden pike u understand?
maiden pike
<@486171952600580116> u understand?
im here now so sorryy
torn jolt
what grade r u in
maiden pike
11
maiden pike
grade 11
maiden pike
oh im canadian
maiden pike
thats cool australia tropical
torn jolt
presonally i would rather be in canada
that snow and ice omg
i wish
anyways let me know if u don't understand what I wrote
maiden pike
wait
maiden pike
12x - 4 is the base
how u get this?
torn jolt
ok
let me write it out for u
i'll draw a diagram
firstly what are the properties of an isosicles triangle
full forumBOT
@maiden pike Has your question been resolved?
full forumBOT
torn jolt
.reopen
maiden pike
.reopen
full forumBOT
✅
full forumBOT
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
@maiden pike Has your question been resolved?
wintry cosmos
ohh lol, I was not aware
maiden pike
.close
torn jolt
i dont really get this
full forumBOT
i dont really get this
devout valley
What's the definition of eigenvector/values you have?
torn jolt
idk, i just think i would maybe do Ax = b?
like reduce [A|x] and that gives an e-vector??
ripe bear
The definition of an eigenvector of a certain matrix is that which is only scaled and not rotated by the matrix. the given vector is scaled by zero and not rotated. hence it's an eigenvector. the scaling factor is called the eigenvalue of that vector. which in this case is zero.
torn jolt
how is it scaled by zero? and what does rotated mean?
ripe bear
how is it scaled by zero? and what does rotated mean?
formally speaking, rotated means it's not a constant multiple of the original vector. concretely speaking it means the vector doesn't visually rotate when you apply the matrix to it. it either extends or contracts.
it's scaled by zero because applying the matrix gave you the zero vector
so the outcome is the old vector multiplied by zero.
torn jolt
.close
mystic cedar
full forumBOT
mystic cedar
just 1 question
when we have to find R and r
when it says about the line y = 1
i get confused wheater to subtract the function by 1 or add
how do u know which one to do
full forumBOT
@mystic cedar Has your question been resolved?
full forumBOT
full forumBOT
Available help channel!
green lily
full forumBOT
green lily
I let z = a+bi and using that i found "a" by equating real and imaginary components
however i don't know how to find "b"
I assume that "Given that this equation has exactly one root" has some significance but idk what
would completing the square on my real part work?