its because cos is smaller than 1
#help-38
quaint gazelle
so 1-cos is bigger than 0
by definition of cos
yeah
you could
since for positive numbers
x=|x|
fathom ivy
because sin can be negative
but it has to be positive
so you take the abs value to force it to be
yes
the full working out should involve putting abs value on both and then you remove the abs of 1-cos because it's completely unnecessary
good habit
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wraith hinge
dense zealot
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trail ingot
it could just be part of the name of the variable
trail ingot
never seen that before then 🤷♀️
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wide gyro
can someone help me out, I need to completely factor each polynomial over real numbers and find its roots and simplify my answer: f(x) = 2x^4+x^3-35x^2-113x+65
inland orbit
Do you know the rational root theorem?
wide gyro
Do you know the rational root theorem?
yes
I tried using a graphing calculator to find the zeros but I think I'm doing it incorrectly because I can't seem to find them
inland orbit
You couldn't find any?
wide gyro
You couldn't find any?
I might be setting the wrong bounds, like the left and right
I'm not sure, but yeah I fail to find any
inland orbit
wide gyro
which one should I use
inland orbit
Both, probably
Your polynomial is degree 4, if you divide by both linear factors, you'll get a quadratic
It appears the other two roots are non-real, so you won't be able to factor the quadratic in the reals
wide gyro
yeah you kind of lost me there, but I'm gonna try to use 0.5 to divide thank you
inland orbit
Use 0.5 how?
wide gyro
Use 0.5 how?
synthetic division?
inland orbit
Sure, to divide by (x-0.5), right?
wide gyro
Sure, to divide by (x-0.5), right?
yes
inland orbit
I just meant, after that, you'll probably want to also divide the result by (x-5)
That's what I meant by use both
wide gyro
I just meant, after that, you'll probably want to also divide the result by (x-5...
ohhh okay see now that makes more sense
I couldn't understand what you said before, it didn't feel like it was in english
my bad
inland orbit
Lol sorry
wide gyro
nah i'm just dumb
inland orbit
Every time you divide by something like (x-k), the degree goes down by 1. You're starting with something of degree 4 (since it's x^4), so you'll need to divide by both to get it down to degree 2
wide gyro
Every time you divide by something like (x-k), the degree goes down by 1. You're...
yeah that makes sense now, thank you
inland orbit
Which is what you want, degree 2 is something you can deal with with the quadratic formula or whatever
No problem 👍
rugged latch
not sure how to do this, or where to start
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not sure how to do this, or where to start
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zinc ginkgo
not sure how to do this, or where to start
did you find the eigenvalues?
rugged latch
Yes I found them to be -1 and 7
rugged latch
eigenvectors?
So I found the reduced matrices, but I’m not sure how to get the eigenvectors from them. Here’s a picture. It feels so simple but I’m having a brain freeze.
rugged latch
https://inst.eecs.berkeley.edu/~ee127/sp21/livebook/l_sym_sed.html
Lemme take a look
rugged latch
https://inst.eecs.berkeley.edu/~ee127/sp21/livebook/l_sym_sed.html
hmm, honestly im not really understanding what to do with SED
i think my understanding is very lacking on this subject
solid kilnBOT
riemann
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loud plover
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loud plover
I know messed up somewhere just don't know where
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grand lark
Hi, I'm having trouble understanding the part how 2det(A) = 0. Can someone explain that to me?
zinc ginkgo
Hi, I'm having trouble understanding the part how 2det(A) = 0. Can someone expla...
what numbers x satisfy x = -x ?
zinc ginkgo
,calc 3
solid kilnBOT
Result:
3
,calc -3
solid kilnBOT
Result:
-3
AHAHAHAH ok I see
x = -x
2x = 0
Man I hate it when these abstract things block my mind from simple algebra
Tytytyt
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remote beacon
Confused on how - 3²⁸ / 3³⁰ equals - 1/3²
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Confused on how - 3²⁸ / 3³⁰ equals - 1/3²
remote beacon
(whole fraction is negative)
random citrus
30-28 = 2
stoic saddle
n^a / n^b = n^(a-b)
stoic saddle
1/n^b = n^(-b)
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wraith hinge
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wraith hinge
Is there a way to write this as a decimal?
Itried to simplify so far
<@&286206848099549185>
The x and y confuses me do i need to do sonmethibg to get rid of them
zinc ginkgo
Is there a way to write this as a decimal?
no there isn't
x and y are unknown variables and you have to leave them as variables
wraith hinge
x and y are unknown variables and you have to leave them as variables
Is there no way to find the variables ?
wraith hinge
and explicitly told to plug them in
I thought maybe you could change the positions so you have x = y +...... for example and then input this for x to find y and then input numbers for x and y maybe
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stoic iron
Look harder
silent canyon
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languid pier
it says its right?
trim joltBOT
it says its right?
languid pier
oh just use the other ones?
stoic saddle
im presuming so
languid pier
mk
stoic saddle
values of f to me says f(x_min) f(x_max)
languid pier
worked ty
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stoic saddle
understandable
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clever slate
did I do this wrong or something
zinc ginkgo
holy
can you just use the geometric series
$\frac{1}{1-(-x)} = \sum_{k=0}^\infty (-x)^k$
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riemann
delicate lance
How do I prove this ?
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lament jewel
hi
delicate lance
hi
lament jewel
well
lethal anvil
hi
delicate lance
hi
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full dock
Can someone check this if it’s wrong or correct?
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@full dock Has your question been resolved?
steady moth
you forgot to divide x by /2
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full dock
@steady moth
kindred pier
What does If cos(x/2) apply mean?
rugged latch
Maybe it’s: if f(x) = cos (x/2)
wraith hinge
Ur my only hope
rugged latch
@wraith hinge #❓how-to-get-help
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wraith hinge
kindred pier
What makes you so special to take someone else's channel?
steady moth
<@277264404213399553>
yup now just simplify
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stiff crescent
hello, i was wondering if i could get some help in proving a function f is surjective?
stiff crescent
is it as simple as supposing some b in the codomain of f such that f(a) = b, then working backwards to show that a is, indeed, in the domain of f?
stoic iron
you need to pick an arbitrary b in the codomain, and show b = f(a) for some a in the domain
stiff crescent
you need to pick an arbitrary b in the codomain, and show b = f(a) for some a in...
that means i have to choose an a in the domain right?
in practice, do i basically solve for a in terms of b, then show that that solved term is indeed in the domain?
marble wharf
yes
well depends on the function of course, but that is definitely a viable strategy in a lot of cases
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stiff locust
So in a linear relationship
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So in a linear relationship
left oriole
depends on the power series, because power series can represent a wide range of possible functions
could be a constant function, linear, any polynomial, an exponential, a cosine or sine, etc
left oriole
could be a quadratic (parabola)
depends on the exact values of the points
5 points uniquely determine a 4th order polynomial, so that would certainly work
stiff locust
So for linear I wrote
The mathematical relationship is linear where acceleration is increasing by a constant amount
left oriole
if it were linear, the graph would look like a line
stiff locust
What about this?
The mathematical relationship is a power series where acceleration..
no its for different one
left oriole
yea like that one
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wraith hinge
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modest rampart
what u want help with as in where are u stuck
wraith hinge
Can u explain me the sum please
modest rampart
for this type of question i will tell u step to go thru it easily
first open the brackets (like multipying 1/6 and 2/3 with their respectives
then transfer variables to one side and constant to other
solve it
wraith hinge
Ok thank you
zinc ginkgo
,rotate
solid kilnBOT
left oriole
,rotate
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left oriole
a reasonable first step would be to clear the denominator (multiply both sides by x-5)
wraith hinge
I can't really understand can u show in a paper please
left oriole
multiply both sides by x-5, you don't understand that?
wraith hinge
Ok can u say next step
left oriole
simplify both sides and rearrange into the form ax^2 + bx + c = 0
wraith hinge
Btw it's linear equations
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dense agate
Hi!
mellow hull
Ask
dense agate
and sorry it’s just a test
mellow hull
Yea just ask
dense agate
so we are doing equivalent fractions lemme screen shot it rq
mellow hull
Okay
hazy light
If you want the decimal equivalent, it's 0.75
mellow hull
Thatss equal to 3k/4k
dense agate
so like lemme show you
it’s comes with this
so it’s not just any equal number .
1/8?
maybe?
mellow hull
Okay so on the left you have 3 parts out of 4
shell radish
you got 8 pieces on the other thing so to equal it you'd multiply your first fraaction by 2
leaving you with 6/8
hazy light
Multiply and divide 3/4 by 2
mellow hull
On the right you have some parts out of 8
dense agate
yeah so wouldn’t it be 1/8?
mellow hull
"A single part of the first diagram is equivalent to two parts in the second diagram"
dense agate
is it 1/8?
mellow hull
yeah so wouldn’t it be 1/8?
No
night zodiac
yeah so wouldn’t it be 1/8?
No, because the left pie has 4 parts, the right has 8 parts
dense agate
I shaded the left one
mellow hull
"A single part of the first diagram is equivalent to two parts in the second dia...
So 3 parts in the first diagram wud be equal to to 6 parts in the second diagram
night zodiac
I shaded the left one
You have 3/4, how can you make that into 8 parts?
night zodiac
So 3 parts in the first diagram wud be equal to to 6 parts in the second diagram
Really, stop giving out answers
mellow hull
Really, stop giving out answers
Dude atleast this is 'explaining'
mellow hull
"A single part of the first diagram is equivalent to two parts in the second dia...
Look
shell radish
everyone calm down and help with my question 💀 . naw im playing but the first "pie" is cut into 4 equal pieces and the second is cut into 8 equal pieces. if both pies are the same size then that means one piece of the first pie is equal to two pieces of the second pie
and since you have a total of 3 pieces out of 4
that means in the second pie, youd have 6 pieces out of 8
night zodiac
First, you have $\frac{3}{4}$ on the left pie, on the right pie, it's out of 8. The out of part, is the number in the denominator, aka the total amount of pieces you have. What do you need to multiply by, to make that 4 into 8?
solid kilnBOT
dldh06
night zodiac
that means in the second pie, youd have 6 pieces out of 8
Did you not see what I stated above to the other user? Don't give out answers
shell radish
sorry dad
dense agate
that means in the second pie, youd have 6 pieces out of 8
ty
<@&286206848099549185>
If 6(x+4)=36, what is the value of x+4?
night zodiac
Set it equal to x + 4
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toxic sigil
rugged latch
looks right to me
toxic sigil
looks right to me
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harsh flower
How would I solve this
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How would I solve this
harsh flower
<@&286206848099549185>
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verbal fable
how do i simplify [xe^(10lnx)]
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how do i simplify [xe^(10lnx)]
cerulean ember
a*ln(x)=ln(x^a)
solid kilnBOT
Modus
delicate bobcat
cerulean ember
What's confusing you?
verbal fable
idk how to apply those rules
the question was to differentiate it
he solved it like this
question 26
verbal fable
What's confusing you?
.
nvm nvm
i got it
e cancels ln
and 10lnx = x^10
so its x * x ^ 10
= x ^ 11
Thank you @cerulean ember @delicate bobcat
cerulean ember
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lament ermine
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austere cove
Does image of linearly transformation is also called as projection?
zinc ginkgo
Does image of linearly transformation is also called as projection?
is every linear transformation also a projection?
austere cove
No
austere cove
Does image of linearly transformation is also called as projection?
If no then what's the difference between these two? actually want to know what is image of linear transformation
zinc ginkgo
If no then what's the difference between these two? actually want to know what i...
you mean the definition of image? it's just the set of all points the transformation maps the domain to
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austere cove
you mean the definition of image? it's just the set of all points the transforma...
Then what is kernel about , isn't it gives the same points of transformation corresponds to the domain
austere cove
Then what is kernel about , isn't it gives the same points of transformation cor...
I am asking the difference in simple terms not in definition
austere cove
Why kernel and where it is used , need an example relates to real life scenario say like in data science we split data or obtain insights in it like that
zinc ginkgo
Just google examples?
austere cove
Anything just wanna understand the concept
austere cove
I can't message there
zinc ginkgo
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surreal harness
would I use permutation or combinations here?
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would I use permutation or combinations here?
rare nexus
Combinations
surreal harness
i used brute force to get 4 ways, but what is a step I can take to get started
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surreal harness
no I still need help <@&286206848099549185>
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wraith hinge
"It is given that m% of the students wait between r minutes to s minutes to get on the bus. State the value of m."
wraith hinge
Why is the answer 50? Since it is between r and s minutes, it can be 50 or 75 right?
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wraith hinge
What am I doing wrong?
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What am I doing wrong?
fathom ivy
what’s larger, (n-6)! or (n-5)!
fathom ivy
rest looks good
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warm sierra
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warm sierra
Eigen value checking if Mine is correct? As online calculator has different value
Can someone please help out
slender shard
You forgot to subtract -12 in the second column from the 2nd row to the 3rd row.
And in the first column, third row; -(-5) = 5.
warm sierra
slender shard
Yes, it should be positive.
warm sierra
Nd abt the 12 was there an error there?
warm sierra
Did u solve this just now?
slender shard
Yeah.
warm sierra
Thank youuuu so muchhh ur acc a lifesaver Ty appreciate a lot
Thank you once again
slender shard
yw
warm sierra
🙏
dense zealot
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dense zealot
hi can any explain maybe how to get from the clue part to why it's 1* k* 1
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warm sierra
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warm sierra
Is my rref correct?
wraith hinge
Seems... Fine
warm sierra
Fr? Because I had it wrong bfr and I did this again
wraith hinge
,w RREF {{-4, 12}, {-1, 3}}
solid kilnBOT
warm sierra
Yoooooo
warm sierra
,w RREF {{-4, 12}, {-1, 3}}
Thank you
wraith hinge
Ofc
warm sierra
But also then here the eigen vector is 3,1 which wld be correct in the previous rref and not this
Must be doing something wrong
I think this is error ?
,w RREF {{-3, 12}, {-1, 4}}
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warm sierra
I think this is error ?
Help needed here *
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scarlet escarp
I think this is error ?
why did you subtract -3v_2
the equation would be v_1 - 3v_2 = 0
warm sierra
If I had +3 wld the equation still be -3v_2 or then it wld be +3v_2
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warm sierra
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scarlet escarp
so your matrix equation states
v1 - 3v2 = 0
so v1 = 3v2
this your vector should be [3 1] as the one from wolfram alpha
warm sierra
this your vector should be [3 1] as the one from wolfram alpha
Corrected now thank you
scarlet escarp
which formula
warm sierra
I just had the question regarding the formula
is the formula v_1 - []v_2 = 0 …. Is there always -ve sign there irrespective of the number
scarlet escarp
do you know how matrix multiplication works? in particular matrix-vector multiplication
this is no different
scarlet escarp
think of it as always adding, but we can change the sign of the coefficient
so if it was -3
it would be v1 + (-3v2)
which as you know
is just v1 - 3v2
warm sierra
Yes
scarlet escarp
if you prefer to think of pluses in front of the constants i’m sure that’s fine
warm sierra
If the coefficient is a positive number then it would just be addition sign there
Since + + = +
scarlet escarp
err not exactly, but it works
it’s really just a 3, and matrix multiplication calls for addition
but again if it works for you run with it
warm sierra
it’s really just a 3, and matrix multiplication calls for addition
That. got it
Thank you
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true oar
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rapid kiln
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rapid kiln
for this question i made 3x - 4y = 35 and x - 2y = 15
which i ended up getting y = -5 and x = 5
so is that a and b cause in that case the answer is 0
past widget
which part about After 15 mins, ping helpers do you not understand?
rapid kiln
my bad
past widget
Anyways, yeah your answer is right
rapid kiln
ok thank you
past widget
v = (5, -5) and a + b = 0
rapid kiln
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strong horizon
Could any1 help me with this problem? I was having difficulties with it yesterday
strong horizon
Just to clarify, we’d get this, right?
stark bison
First find y'(4)
strong horizon
First find y'(4)
Are my derivatives in that screenshot correct?
stark bison
Eh, did you get y' = 4^(x^2 - 5x + 5) * (2x - 5) * ln4 ?
strong horizon
Eh, did you get y' = 4^(x^2 - 5x + 5) * (2x - 5) * ln4 ?
I did!
strong horizon
Then it's correct
Just to make sure, the derivative of 4^x is ln(4), right?
stark bison
Derivative of 4^x is 4^x * ln4
strong horizon
Derivative of 4^x is 4^x * ln4
Got it. And then I solve for m, and plug it back into slope intercept form?
stark bison
Yeah you just find m and then find the free constant so that the tangent actually crosses the graph
strong horizon
Yeah you just find m and then find the free constant so that the tangent actuall...
What is the free constant? Do you mean what x equals?
stark bison
y = mx + b, b here is the free constant
strong horizon
y = mx + b, b here is the free constant
So do I also have to solve for b?
strong horizon
What did you get for y'(4)?
Let me solve for it rq.
strong horizon
What did you get for y'(4)?
We do chain rule for y prime of 4, right?
stark bison
We did* that, now just plug x = 4 into y'(x) = 4^(x^2 - 5x + 5) * (2x - 5) * ln4
strong horizon
We did* that, now just plug x = 4 into y'(x) = 4^(x^2 - 5x + 5) * (2x - 5) * ln4
I get 32ln(4)-5..
strong horizon
We did* that, now just plug x = 4 into y'(x) = 4^(x^2 - 5x + 5) * (2x - 5) * ln4
Then what do we do? That’s our m, right?
stark bison
You should have gotten 12ln4 though
stark bison
Then what do we do? That’s our m, right?
Yeah, 12ln4 is our m
strong horizon
Yeah, 12ln4 is our m
I got 32ln(4)-5…can I show you my work?
stark bison
$4^{4^2 - 5\cdot{4} + 5}\cdot{(2\cdot{4}-5)}\cdot{\ln{4}} = 4^1 \cdot{3}\cdot{\ln{4}} = 12\ln{4}$
solid kilnBOT
A Lonely Bean
strong horizon
$4^{4^2 - 5\cdot{4} + 5}\cdot{(2\cdot{4}-5)}\cdot{\ln{4}} = 4^1 \cdot{3}\cdot{\l...
Got it, so that’s our m?
stark bison
Yes
So y = 12ln4 * x + c for some number c
We gotta solve for c now
We need 12ln4 * x + c to have the same value as y when x = 4
So 12ln4 * 4 + c = y(4)
48ln4 + c = 4
c = 4 - 48ln4
So the tangent line is y = 12ln4 * x + 4 - 48ln4
Which can be nicely written as y = 12ln4 (x - 4) + 4 actually
strong horizon
So 12ln4 * 4 + c = y(4)
Wait, why do we do *4, and why do we set it equal to y(4)?
stark bison
y = 12ln4 * x + c needs to cross the point (4, y(4))
strong horizon
Why do we multiply 4 by 12ln(4)?
stark bison
Meaning that if we plug in x = 4 and y = y(4) then the equation will still be true
stark bison
Why do we multiply 4 by 12ln(4)?
We plugged x = 4 into the equation
strong horizon
Ight gtg now
Wait,why do we change y(4) to 4?
Last question
<@&286206848099549185>
<@&286206848099549185>
whole coral
Wait,why do we change y(4) to 4?
Substitute x=4 into the equation for y
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strong horizon
Substitute x=4 into the equation for y
I’m not following
We substitute 4 into the equation?
whole coral
We substitute 4 into the equation?
Yea $y = 4^{x^{2} - 5x + 5}$
solid kilnBOT
chartbit
whole coral
y(4) is y when x=4
strong horizon
Yea $y = 4^{x^{2} - 5x + 5}$
Still not following, can you break this down more? Y(4) is y when x=4?
What does this mean?
whole coral
What does this mean?
Basically it's notation - sometimes y is represented as y(x) (to show that it's a function of x)
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whole coral
In any case, you want to find out what y = ... is equal to when x=4
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eternal gull
Is this the right answer, 49?
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Is this the right answer, 49?
long basin
old pebble
Quite the username...
eternal gull
Quite the username...
i thought this was about math not my username
eternal gull
you just forgot the last step
whats the last step
eternal gull
5x * x = 245
5x*49=245?
fresh pecan
no
old pebble
What are your steps?
eternal gull
What are your steps?
i did 245=5x then divided 5 by 5 which is just X then divided 245 by 5 and got 49
fresh pecan
245 is not 5x
old pebble
5x is a line here
eternal gull
what do i do
old pebble
i thought this was about math not my username
With a name like this youve got to be prepared for the ensuing laughter especially on the internet
old pebble
what do i do
Equation for a rectangles area?
eternal gull
With a name like this youve got to be prepared for the ensuing laughter especial...
dont see anyone laughing but alright
I thought yall could help me step by step but it doesnt seem like im getting any help i have to study for this test and Idont even know all the steps its not like i can just pull them out of my bum like magic, guess Ill seek help elsewhere
eternal gull
With a name like this youve got to be prepared for the ensuing laughter especial...
and ofc you would laugh ur literally an everything, lady
what has this generation come to
degeneracy
old pebble
🤣
fresh pecan
what has this generation come to
you realize its just a vocal minority who wants this
old pebble
Dude you're the one who's getting mad
eternal gull
Dude you're the one who's getting mad
eternal gull
i remember being an edgy teen lol
Im not being edgy. unlike the rest of the newgen weirdos (you) I embrace masculinity
yall are soft as flies
little gay femboys
old pebble
You are the one afraid of being gay lol
old pebble
That sounds pretty beta male to me
eternal gull
https://tenor.com/view/andrew-tate-be-a-man-gif-25846216
@old pebble be a man do some pushups
old pebble
MAN LIFT ROCK, STRONG MAN IN VILLAGE
eternal gull
bet its lower than mine
what does that matter? Id still f*ck you up in a fight, i do MMA (Muay Thai, Boxing, Jiu Jitsu)
old pebble
he does it all
fresh pecan
bro you weigh 135 lbs time to shut up
old pebble
He's ready to throw down in case anyone tells him he might like men
eternal gull
bro you weigh 135 lbs time to shut up
Even if I did weigh that much I would still slap the fuck out of you and you wouldnt do sh1t about it
mystic forge
wtf has this become
eternal gull
https://tenor.com/view/hasbulla-kick-angry-fight-fail-gif-21699142
thats hasbulla the goat
comparing me to the goat
old pebble
We are truly being epicly owned
eternal gull
We are truly being epicly owned
corny
mystic forge
Is this the right answer, 49?
formula of area of rectangle = length x breadth
here length is 5x, breadth is x
so area will be 5x . x = 5x^2
5x^2=245
x^2=49
x=7
longest side = 5x = 5*7 = 35
eternal gull
formula of area of rectangle = length x breadth
here length is 5x, breadth is x
...
THANK YOU
unborn cipher
I like you @eternal gull , in a very very straight way
eternal gull
I like you <@1021607530218135664> , in a very very straight way
W
unborn cipher
lol. Ok good
old pebble
He will stare at the man for hours but it's normal behavior
unborn cipher
doesn’t sound like straight behavior
eternal gull
this doesnt sound like straight behavior
mystic forge
this doesnt sound like straight behavior
this definitely doesn't scream satire either
eternal gull
this definitely doesn't scream satire either
It would be funny if you believed that, defend the lady as much as you want
eternal gull
I mean, i dont think any non soft straight man or woman would setup a pronouns page just for satire
old pebble
Burn me at the stake
unborn cipher
clogger
lol
mystic forge
I mean, i dont think any non soft straight man or woman would setup a pronouns p...
did you give up a second of your life to read that page?
eternal gull
did you give up a second of your life to read that page?
i may have glanced over it no more than half a second
old pebble
If he looks at it too long he might contract being gay from me......
eternal gull
old pebble
Really into the muscular men huh
unborn cipher
ok this Andrew Tate obsession is getting out of hand
old pebble
It's amazing kids actually think he's what they should aspire towards
mystic forge
the only good thing that came out of tate's existence is that I discovered Indila because of him lol
unborn cipher
India? wdym
mystic forge
India? wdym
the one who originally made his theme song
well tate has a "theme song" associated with him
that songs singer is Indila, who is amazing
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tidal crane
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tidal crane
This is what i worked out, but in the solution of the problem they let
delta = min {1, 3/2 epsilon}
I don’t really understand why it has to be the minimum of the those two and not just 3/2 epsilon?
whole coral
I don’t really understand why it has to be the minimum of the those two and not ...
E.g. set $\varepsilon = 6$ - then $|x|<\delta = 9$, but that doesn't guarantee that $|x|<1$, as is a key part in your proof
solid kilnBOT
chartbit
whole coral
Setting $\delta$ to be the minimum of both means that $|x|$ will be less that both of those values (1 and $\frac{3\epsilon}{2}$)
solid kilnBOT
chartbit
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tidal crane
E.g. set $\varepsilon = 6$ - then $|x|<\delta = 9$, but that doesn't guarantee t...
Ohhh got it, makes sense. Thank you so much!
coral viper
What number gives a result of −3 when 8 is subtracted from the quotient of the number and 5?
Im not really good with these kinds of word problems if someone could help me that would be great!
coral viper
As far as I know it has to start with -3=
And I think quotient is divide but idk how to apply that
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stable comet
What are the points for 3x^2-5x+1
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What are the points for 3x^2-5x+1
stable comet
On a graph
Ik the vertex is 5/6,-13/12
This is the equation in vertex: 3(x-5/6)^2 -13/12
<@&286206848099549185>
tepid junco
stable comet
Hey
The vertex is correct right
I just need to find the other points on the graph all i have is the vertex
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@stable comet Has your question been resolved?
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@stable comet Has your question been resolved?
stable comet
<@&286206848099549185>
cyan zinc
Electrify
stable comet
Yea
queen yarrow
Yo
stoic iron
do the computation
solid kilnBOT
queen yarrow
Lowkey my teacher probably over did it here
stoic iron
or if you know anything about how tranpose interacts with dot product then use that
queen yarrow
Is this even linear algebra
stoic iron
yes this is definitely linear algebra
queen yarrow
Lol
O I see
Is it this or am I dumb
I put w1 is 1 and w2 is 2
It gives same thing at the end so the equality is true I guess
Feels this is too simple and wrong
amber python
w1 and w2 are vectors
boreal dome
I put w1 is 1 and w2 is 2
wrong
boreal dome
w1 et w2 sont des vecteurs
amber python
you should prove it in general
amber python
just write w1 and w2 as two general vectors
boreal dome
$\begin{pmatrix} x \ y \end{pmatrix}$
solid kilnBOT
Ｈｅｒｅｌｓ
boreal dome
for example
amber python
say w1 = (x, y), w2 = (z, w)
queen yarrow
Oh also
Ok
I’ll do that
Brb
Is it this
Well whatever last question
Surely this is just bullshit?
Bro said derivative w and w is some orthogonal?
O I see
So w is = (cos Teta, sin teta)
We gotta show w times it’s derivative = 0
Can anyone confirm that’s it’s this
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wraith hinge
Linear equations grade 8
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Linear equations grade 8
wraith hinge
,rotate
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random river
how do you work out if congruences are fulfilled?
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how do you work out if congruences are fulfilled?
random river
for example 13 = 124 (mod 37)
upbeat lynx
124 / 37 = 3 + 13 / 37 so it's 13 mod 37
stoic saddle
can you also do (13-124 )/ 37, which is -3 and show that since there is no remainder ?
upbeat lynx
not really good at this tbh but I believe a = b (mod k) is the same as a - b = 0 (mod k) so showing a - b has no remainder when divided by k should work
a = b (mod k) <=> a = mk + l and b = nk + l <=> a - b = (m - n)k + 0 <=> a - b = 0 (mod k)
I hope this reasoning is right
vast goblet
hi
vast goblet
what is √ of 72164823845
split chasm
,calc sqrt(72164823845)
solid kilnBOT
Result:
2.6863511282965e+5
@vast goblet Has your question been resolved?
glacial kelp
help
glacial kelp
can someone quickly check my work on this?
convert the decimal number 257 to 8-bit unsigned binary
since 257 is larger than 8 bit
do i just chop off the MSB and make it 00000001? so 1 basically?
visual dome
glacial kelp
ok, I tested with an online calculator and it did that, so just making sure because the calculator website looked older than my blood line, thanks
!solved
!close
idk how to close lol
.close
wraith hinge
If 1/y-x;1/2y and 1/y-z are three consecutive terms of an arithmetic sequence prove that x, y and z are three consecutive terms of a geometric sequence
wraith hinge
If 1/y-x;1/2y and 1/y-z are three consecutive terms of an arithmetic sequence pr...
i understand nothing
help me
twin swan
if they are an arith seq then $\f{1}{y-x} + d = \f{1}{2y} \ \f{1}{2y} + d = \f{1}{y-z}$
rip
wraith hinge
.reopen
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✅
wraith hinge
Okey
twin swan
basically you know 1/(2y) - 1/(y-x) = 1/(y-z) - 1/(2y)
wraith hinge
yes
twin swan
it comes from the fact that the differences in AP are constant
wraith hinge
$1$
twin swan
okay, so doing common denominator stuff
you can massage it into a form thats much nicer
wraith hinge
it comes from the fact that the differences in AP are constant
what AP mean im not english ?
twin swan
arithmetic progression
aka arithmetic sequence
anyway this is what it boils down to
once you do all the simplifying
wraith hinge
yeah its like b²=a*c
twin swan
now i'll show they are a geometric sequence
let y = x*r, z = x*r^2
then the left side turns into x^2 r^2 and RHS turns into (x*r)^2
which is also x^2 r^2
that means it is a geometric sequence
twin swan
let `y = x*r, z = x*r^2`
since this is the definition
wraith hinge
i have a question
twin swan
ask
wraith hinge
where is the square from the y ?
wraith hinge
twin swan
that happens when simplifying
wraith hinge
Ok
twin swan
these two forms are identical
wraith hinge
let `y = x*r, z = x*r^2`
and here the r is the reason ?
wraith hinge
but its only for x y z or for the all fraction like 1/y-x;1/2y and 1/y-z
twin swan
you showed that the fraction being in AP implies xz = y^2
so now you show x,y,z is geometric
twin swan
you showed that the fraction being in AP implies xz = y^2
based on xz=y^2
wraith hinge
but wait
1/y-x is a1 for AP and y x and z is for GP ?
y-x is the a1 for GP ?
@twin swanhey
twin swan
yes 1/(y-x) was for AP
we showed that since it was AP, using the AP equations we got xz = y^2 and that only concerns x,y,z
and thats a geometric sequence
wraith hinge
but i need to find x y z or no ?
wraith hinge
then the left side turns into `x^2 r^2` and RHS turns into `(x*r)^2`
after this is done ?
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frail current
Friday, with each dinner being at one of his ten favorite restaurants.
(a) How many possibilities are there for Fred’s schedule of dinners for that Monday ```can anyone explain this question for me?
restive drift
Is that the entire question? Only Monday?
for part a
cuz he only has 10 choices is it’s just Monday
restive drift
Am I seeing it correctly?
frail current
yes
restive drift
This would just be 10 if it’s only on Monday
frail current
what is the question asking though
oh snap
wtf
if he has 10 total favorite restaurants
to choose from for the first day
the number of possibilities for that day is 10
restive drift
Yes
frail current
why was this hard for me to comprehend the first time
through Friday, if Fred is willing to eat at the same restaurant more than once, but is
not willing to eat at the same place twice in a row (or more)?```since he cant eat back to back restuarants the following day will always be 9
10-9-10-9-10
restive drift
Yes but how did you get 10 for wed and fri
frail current
because after tuesday i can choose the same restuarant i chose on monday, same applied with the latter
restive drift
Yes but you can’t choose the restaurant you chose on Tuesday
frail current
yes
restive drift
You can go to Monday’s restaurant on Wednesday
But not the one you chose on Tuesday
frail current
oh snap so itll be 9 for both wed and friday then
restive drift
Yes
frail current
since i cant choose back to back days
frail current
yeah i missed that case
restive drift
Just make sure to fully understand the problem before jumping in and you’ll be good
frail current
ty
@restive drift sorry i messed up for the first part
i didnt paste full question
restive drift
yw
frail current
through Friday, if Fred is not willing to eat at the same restaurant more than once?```No worries
frail current
this is the full question
restive drift
How would you do this one?
frail current
10-9-8-7-6
restive drift
Yep that’s correct
frail current
we just multiply those to get our solution
restive drift
Yep since we start off with 10 choices for day 1 and lose a choice a day
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jovial sluice
Someone can help ?
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Someone can help ?
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jovial sluice
,reopen
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