is it above or bottom
#help-23
humble grove
thin bridge
what's the length of the side opposite that
humble grove
a/sina=b/sinb
thin bridge
and what letter would that be represented by
thin bridge
no
humble grove
18 b
thin bridge
no
thin bridge
doesn't seem to be answering the question I initially asked
thin bridge
which letter represents the side opposite the 110° angle A
humble grove
then ill study. based off my notes
humble grove
which letter represents the side opposite the 110° angle A
b
thin bridge
no
from labelling convention, the lowercase letter represents the side opposite the respective capital letter angle/vertex
humble grove
A?
thin bridge
ok so A = 110,
a = 18
humble grove
agrred
thin bridge
<ACB or simply <C or C here is currently unknown
humble grove
mhm
thin bridge
what's the length of the side opposite that
and what's the lowercase letter that represents it
these are not supposed to be trick questions
humble grove
yeah
thin bridge
we don't really care about b here
humble grove
side opposite B is b
thin bridge
ok so A = 110,
a = 18
c = 8
C is currently unknown so just leave it as C
now plug those values into the sine rule
thin bridge
now plug those values into the sine rule
humble grove
18/sin110=8/sin C
thin bridge
where's x coming from
humble grove
i meant c
humble grove
and then use inverse sine to determine C
r u kidding me
thin bridge
to get something in the form
sin(C) = whatever
the equation that tells you exactly what sin(C) is
similar to when asked to solve something for x, you end goal/result is an equation telling you exactly what x us
thin bridge
how are you getting 26.4
thin bridge
starting with
18/sin110=8/sin C,
do not touch your calculator yet,
manipule that equation algebraically
humble grove
how do i solve ac
thin bridge
sin(C) =
humble grove
how do i solve ac
thin bridge
AC is given
thin bridge
angle sums to determine the thirr angle
humble grove
starting with
18/sin110=8/sin C,
do not touch your calculator yet,
manipule that...
sin110x8=18C
thin bridge
no
thin bridge
what happened to the sin attached to the C
thin bridge
the principle is exactly the same
thin bridge
the principle is exactly the same
humble grove
find AC
how
how do i find AC
what would the formula be
just write out the equation
and i'll follow along
thin bridge
angle sums to determine the third angle
humble grove
starting with
18/sin110=8/sin C,
do not touch your calculator yet,
manipule that...
write out the angle like u did here
C is 40
@thin bridge
@thin bridge
@thin bridge
@thin bridge
@thin bridge
thin bridge
yes applying angle sums C = 40 here
thin bridge
now go through exactly what I walked you through before
humble grove
JUST WRITE THE FORMULA I HAVE TO GO DUDE
WRITE THE EQUATION
PLEASE
MY BLOOD LEVELS ARE HIGH BC OFU
thin bridge
identify angles and sides you know and are trying to determine and plug them into the sinevrule
FFS this rudeness
thin bridge
I'm out and blocking you niw
ionic brook
what happened here lol
safe radishBOT
@humble grove Has your question been resolved?
hollow torrent
what happened here lol
rip
safe radishBOT
hollow torrent
MY BLOOD LEVELS ARE HIGH BC OFU
at least we know his "blood levels are high"
bless this person
safe radishBOT
Available help channel!
toxic viper
I know how to factorize, but i just dont know how they get to this step.
lost maple
that’s a difference of percent squares
spice grove
Difference of squares, yeah.
plucky elk
(a-b)(a+b) =a^2-b^2
toxic viper
.close
humble mesa
can someone explain what happened?
safe radishBOT
can someone explain what happened?
humble mesa
the rewrite using trig identities part
quasi bison
sin^2(θ) = 1 - cos^2(θ)
safe radishBOT
@humble mesa Has your question been resolved?
turbid canyon
tall hatch
ive been patient for 30 mins
damn u very rude
safe radishBOT
damn u very rude
trim trench
maybe close this @tall hatch
thought I agree it is quite rude
sacred stream
Hi… may i know where i went wrong??? The correct answer is 2
safe radishBOT
Hi… may i know where i went wrong??? The correct answer is 2
fierce ore
For starters
On line 2
You didn't distribute the 4 properly
Wait no I'm dumb nvm that
sacred stream
you just threw away the log without properly handling both sides
I shifted the log on LHS to RHS so i can divide 50x^2
Wait
tired imp
not that
sacred stream
I mean RHS to lhs
sacred stream
Mhm
tired imp
but then you get this. where did the log go?
odd thistle
how did it become 1/202.52
safe radishBOT
how did it become 1/202.52
glass sonnet
divide top and bottom by 24.69
flat frigateBOT
delicate sierra
yea
raw wagon
Small question for what do u use this its about statistic
safe radishBOT
Small question for what do u use this its about statistic
raw wagon
?
quasi bison
nothing can be said about this without context, but
by the looks of it, all that is being shown here is that the sum of the deviations of a dataset from its own mean is zero
if you're specifically looking for a "use" for this, you could try and use it to check if you calculated the mean correctly (if the deviations don't add up to zero you didn't)
safe radishBOT
@raw wagon Has your question been resolved?
sweet bone
For what values of p and q, the function f(x)= 3x^3 + 2x^2 - px + q, the factor of which is x-1, the function of f(-1) = 10?
safe radishBOT
For what values of p and q, the function f(x)= 3x^3 + 2x^2 - px + q, the factor ...
lean chasm
For what values of p and q, the function f(x)= 3x^3 + 2x^2 - px + q, the factor ...
what?
lean otter
-1 + p = 10 - q
lean otter
-1 + p = 10 - q
Your answers dont this
glass sonnet
f(-1) = 10
glass sonnet
it makes sense
lean otter
@sweet bone for every factor
Of a function
The function has a root there
Bla bla
So f(1) = 0
sweet bone
-1*
sweet bone
I did also 8, but not even teachers understood
i went to MATURA exam yesterday and we had this question
but, if u just replace p and q, the result won't be 10, if f(-1)
glass sonnet
$f(x) = 3x^3 + 2x^2 -px + q$
flat frigateBOT
IntelligentCake
glass sonnet
We have full context
glass sonnet
you have one function
glass sonnet
yeah
so do both of those you get 2 equations with p and q
then just solve
simultaneously
sweet bone
@glass sonnet what if we got the function as: f(x)= -3x^3 + 2x^2 + px + q
sweet bone
i changed the - to +
f(x)= 3x^3 + 2x^2 + px + q
this is the function that i got, i forgot that it was with plus
glass sonnet
ok so just carry out same procedure?
sweet bone
lol
f(x)= 3x^3 + 2x^2 + px + q
I just want to know the answer cause it will happen that they review wrongly and i need to make a request about it
@glass sonnet
glass sonnet
I won't tell you the answer
I'm here to help
not give answers
do f(1)
and f(-1)
then sovle
sweet bone
okay
safe radishBOT
@sweet bone Has your question been resolved?
sweet bone
i got
-8 and 3
that would be correct i guess
isnt it
thank you
very much
.close
haughty pollen
the sum of all values of the real parameter for which one root of the equation is twice as large as the other
safe radishBOT
the sum of all values of the real parameter for which one root of the equation...
lean otter
hint: a quadratic with roots $b$ and $2b$ would look like $2(x-b)(x-2b)=0$
flat frigateBOT
Toby
lean otter
**Toby**
if you this expand out, you can equate coefficients with the original quadratic and solve two equations in two unknowns
robust kite
the sum of all values of the real parameter for which one root of the equation...
i would say solve the the quad like normal (consider a is just a number) to solve for x in term of a then apply the Vieta theorem?
safe radishBOT
obtuse jackal
Reflecting about the x-axis means multiplying by -1. Visualize it graphically
glass sonnet
a reflection in the x axis makes the y values negative
you have what y =
you just make that negative
safe radishBOT
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zinc flint
the jacobian here should be -1/2?
zinc flint
<@&286206848099549185>
zinc flint
?
safe radishBOT
@zinc flint Has your question been resolved?
tribal grail
there are 2 points, s and t, both of them are real numbers that differ by 1. the graph of the function fa for a=0.5 has two points: (s|f0.5(s)) and (t|f0.5(t)), they both have the same slope.
find s and t (rounded) and give the slope of the two points for f0.5
safe radishBOT
there are 2 points, s and t, both of them are real numbers that differ by 1. the...
tribal grail
Help xd
glass sonnet
do you mean f(0.5s)
tribal grail
do you mean f(0.5s)
Yes
tribal grail
Yws
glass sonnet
do you have f(x)?
tribal grail
nope
nvm there s one
if a is 0.5 the equation is
x* sqrt of e to the power of x
+1
safe radishBOT
@tribal grail Has your question been resolved?
safe radishBOT
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Available help channel!
south linden
i keep getting the wrong answer, can someone explain how to do this, i think i am approaching it wrong
safe radishBOT
i keep getting the wrong answer, can someone explain how to do this, i think i a...
lean otter
Do you have a cartesian equation of the plane?
safe radishBOT
@south linden Has your question been resolved?
south linden
Do you have a cartesian equation of the plane?
i just miscalculated the cross product, i got it
plucky elk
.close
spice jacinth
Hi guys
final halo
spice jacinth
The problem is the one from above
Is an inequality btw
I need to find the intervals
wise shell
You can do this mathematically by finding when the graph is = 0. and then testing for values that are lower and higher than those two values.
Since, x= -1, 2 make the equation equal to zero, you can plug in -2 into the equation and see what the sign is. Also, plug in 0 as 0 is inbetween -1,2 and then try 3.
wise shell
You know that the equation is 0 when x is either -1 or 2.
So, if you plug in any number less than -1 into the equation what do you get?
spice jacinth
Yeah
wise shell
Choose any number less than -1 and input that as x. Let me know what you get
wise shell
Okay, so that means from (-infinity, -1) The function is positive, AKA >0
Now plug any value between -1 and 2 and tell me what you get.
wise shell
So from (-1,2) the function is negative, AKA less than 0
You can now plug in a number greater than 2, but it's a positive number.
Your interval where the function is less than 0 is (-1, 2). You know this because this is the only values of x where the function takes a negative value.
wise shell
You can always use desmos.com to graph functions and just look at the values it crosses below 0.
spice jacinth
With numbers
For example
(x-1)(x+1)>0
One of those numbers in the equation will be the answer
Right
?
Or am i wrong hahaha
I have a test tomorrow and they don't let us use a calculator or the phone 🤕
wise shell
What you need to do is set each parenthesis =0.
so, x-1=0 and x+1=0
These values shows you where the function is exactly 0.
Now every value before, after, or in-between is either positive or negative. So, you take your two points and select any value below and see what the value is, positive or negative. If it is positive then it is >0. If negative <0.
So if your two numbers let's say are -100 and 100. Your three intervals to test are (-infinity, -100), (-100, 100), and (100, +infinity).
You choose any value for each interval as long as it is in the interval you are testing and input it into the function to see if it is positive or negative.
spice jacinth
Ohh understood
wise shell
If you have something like (x+1)(x+1) then you only test two intervals because both parenthesis yields -1 as the critical point.
AKA the parenthesis are the same thing.
Other than that, you can do this method for any amount of parenthesis. (x+5)(x-3)(x+999)(x+123)
You just end up with more intervals.
spice jacinth
I understand
So I just have to put those two numbers and see if that results on a negative or positive answer
wise shell
What two numbers?
spice jacinth
Of my (x+a)(x-b)
wise shell
You set x+a=0
This gives you the point on the x-axis that crosses 0
so those two numbers when plugged in will make the function = 0.
You have to choose one number that is lower than both, in-between both, and higher than both.
The values of those three "test" numbers tells you if the function is greater than or less than 0.
ripe zephyr
how do i take the factorial of a binomial
safe radishBOT
how do i take the factorial of a binomial
ripe zephyr
like (3n+1)!
buoyant shadow
what's a binomial
ripe zephyr
sum of two terms?
ripe zephyr
hold on are you helping or just asking
buoyant shadow
just asking
to take a factorial of the sum you probably need to know which one is larger 🤔 ?
ripe zephyr
wdym
buoyant shadow
nothing, it's like entertainment until someone who can help sees this
wise shell
I would imagine it would be like (3n+1)! = (3n+1) * 3n * 3n -1 * 3n -2 * ... * 2 *1
ripe zephyr
have no idea
wise shell
That should be right.
worthy hemlock
I would imagine it would be like (3n+1)! = (3n+1) * 3n * 3n -1 * 3n -2 * ... * 2...
It's something like this
ripe zephyr
can you explain
ripe zephyr
yea
wise shell
Okay so (x)! = x* x-1 * x-2 * . . . * 2 * 1.
wise shell
a factorial is taking a number and multiplying one less than the previous number until you get to 1
wise shell
5! = 5 * 4 * 3 * 2 * 1
so you keep subtracting 1 until you get to *1.
Now let x = 3n +1
plug in and you get (3n+1) * (3n+1) -1 * (3n+1) -2 * . . .
ripe zephyr
ok but how do i get to 1 in a binomial
worthy hemlock
It automatically goes to 1, because that's the base case
All factorials will end at one, usually
ripe zephyr
It automatically goes to 1, because that's the base case
i dont understand this
wdym automatically
like i get that it ends at 1
wise shell
Are you asking how do you get down to multiplying by 1 or how do you get rid of the 1 in the (3n+1)?
worthy hemlock
5! = 5 * 4 * 3 * 2 * 1
6! = 6 * 5 * 4 * 3 * 2 * 1, etc
The base case is 1
ripe zephyr
right
buoyant shadow
there's nothing you can do is what they mean, you can't remove the factorial
ripe zephyr
i have to express it as a polynomial
worthy hemlock
I would imagine it would be like (3n+1)! = (3n+1) * 3n * 3n -1 * 3n -2 * ... * 2...
It will look like this, there's not really a way to determine the values in between
ripe zephyr
so what do i do?
wise shell
You should phrase your entire question again.
ripe zephyr
i have to express 3n+1 over 3n-2 as a polynomial
buoyant shadow
you can like, point at the . . . and say this is 3n
worthy hemlock
so what do i do?
First step, clearly ask the question you have. Posting a screenshot/picture of the question you have helps a lot
ripe zephyr
hold on
worthy hemlock
Because asking how to expand (3n+1)! doesn't give much context
wise shell
This?
plucky elk
This?
This is almost your answer
actually that's not even equal to any polynomial
,w (3n+1) choose (3n-2)
flat frigateBOT
plucky elk
Oh nevermind I'm dumb
ripe zephyr
im so lost
ripe zephyr
yes
plucky elk
Write it down and simplify
ripe zephyr
i dont understand the (3n+1)!part
plucky elk
For your values here
plucky elk
Do you know the definition of binomial coefficient?
Are you sure
You need to understand factorials to understand binomial coefficients
plucky elk
its the thing you multiply values by to find a polynomial
Naaaahhhh that's not the definition
Also that's incredibly vague
Look in a textbook for the definition
Or your notes
unique bison
do you understand what this means?
ripe zephyr
3n+1 C 3n-2?
ripe zephyr
how many ways 3n-2 can be chosen out of 3n +1?
flat frigateBOT
giannis_money
ripe zephyr
5 c 2
unique bison
what number is this equal to?
ripe zephyr
10
unique bison
ie. in how many ways can you choose 3 things from 5 things?
yes
how did you get that?
ripe zephyr
i memorized the pascalls triangle till r6
unique bison
how would you find a value you haven't memorised?
unique bison
$\binom{n}{k} = \frac{n!}{(n-k)!k!}$
flat frigateBOT
giannis_money
unique bison
no
plucky elk
so in the case n is a binomial
No n is a number
ripe zephyr
wdym
plucky elk
**giannis\_money**
In this example n = 5 and 5 is a number
ripe zephyr
.close
safe radishBOT
plucky elk
Guess they figured out the definition of binomial coefficient
safe radishBOT
Available help channel!
fierce cosmos
,tex $\frac{r+5}{r^{2}-2r}$ - 1 = $\frac{1}{r^{2}-2r}$
safe radishBOT
,tex $\frac{r+5}{r^{2}-2r}$ - 1 = $\frac{1}{r^{2}-2r}$
flat frigateBOT
tye
ionic brook
which steps are you having trouble with
fierce cosmos
up until this point
it’s out of context but
then the signs become the opposite of before after the last step
ionic brook
not sure what they mean by "change the sign"
but all they did was rearrange the terms
i.e. they moved -r^2 to the front
fierce cosmos
fierce cosmos
why
spice grove
Always simpler to work with a postive leading term.
ionic brook
$\frac{a}{b}=0\iff a=0$
flat frigateBOT
lirmirit
ionic brook
given that $b\neq0$
flat frigateBOT
lirmirit
fierce cosmos
so for the future when i encounter scenarios like this will i just remove the denominator
junior wagon
Might be a dumb question
safe radishBOT
Might be a dumb question
junior wagon
Im trying to prove the second property of group homomorphism
unique bison
@junior wagon how is the 0 power of an element defined in a group?
junior wagon
I've only seeing this for the 0 power of an element in my notes
so the order of $\phi(g)$ is infinite?
flat frigateBOT
Kurama
unique bison
not necessarily
your book should have defined powers of an element
but anyways, it's defined as g^0 = e
junior wagon
your book should have defined powers of an element
as in order of an element?
unique bison
no
junior wagon
unique bison
as in they should have defined what does the notation g^n mean for any integer n
this is a rather trivial matter, you can just assume g^0 = e
junior wagon
ok
thanks
I dont think they defined it
only defined order of an element and order of the gorup
unique bison
Im trying to prove the second property of group homomorphism
do you plan on proving this by induction?
junior wagon
One sec..
safe radishBOT
@junior wagon Has your question been resolved?
flat frigateBOT
Kurama
flat frigateBOT
Kurama
unique bison
yes
junior wagon
right. then multiply both sides by that, then I think that proofs it
unique bison
ye
junior wagon
wait, but why can we take it out?
unique bison
np
junior wagon
.close
safe radishBOT
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Available help channel!
real crater
real crater
<@&286206848099549185>
safe radishBOT
@real crater Has your question been resolved?
glass sonnet
what have you tried
safe radishBOT
@real crater Has your question been resolved?
safe radishBOT
@real crater Has your question been resolved?
vagrant sand
is geometric rv the same as bernoulli rv?
safe radishBOT
is geometric rv the same as bernoulli rv?
@vagrant sand Has your question been resolved?
limber smelt
safe radishBOT
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Available help channel!
pine tulip
Hello guys, i have a question. On this equation $$\sqrt{3}sin^2x+\sqrt{3}cos^2x-2sinx=0$$
safe radishBOT
Hello guys, i have a question. On this equation $$\sqrt{3}sin^2x+\sqrt{3}cos^2x-...
flat frigateBOT
Lyuka
pine tulip
can i do something like this? $$\sqrt{3}\left(sin^2x+cos^2x\right)-2sinx=0$$
flat frigateBOT
Lyuka
pine tulip
If i go on and finish the question i get the correct answer, but i am not sure if what i did can actually be done
compact wraith
Yes you can
pine tulip
oh thats cool, thanks
compact wraith
What step did you think you can;t do?
pine tulip
Since i was leaving "behind" -2sinx, i thought that maybe what i did wasnt actually possible
Well, thanks once again 🙂
.close
agile raven
theta = (L * 2pi) / circumference.... right?
safe radishBOT
theta = (L * 2pi) / circumference.... right?
neat kiln
agile raven
yea, Im trying to do it without r
but thanks, then i just have some computer nonsence going on 😄
.close
safe radishBOT
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Available help channel!
blazing rune
safe radishBOT
blazing rune
what to do in this question?
is finding maximum vlaue of the function given in option work?
i mean i will find maximum of a function and compare it with other other functions maximum .? will it work?
safe radishBOT
@blazing rune Has your question been resolved?
lean otter
i mean i will find maximum of a function and compare it with other other functio...
find the integral of all of those functions and compare
blazing rune
okay
but is there anymore feasible option ?
i mean to do this fastly?
i thought of finding integrals too but...it takes time
.close
tidal nest
safe radishBOT
dull sequoia
what's your question?
dull sequoia
yeah that looks right
tidal nest
What do I do next
dull sequoia
part b?
dull sequoia
you plug in the numbers
you know the function h(t)
and u know the t values
50 and 100
tidal nest
What does that look like again
dull sequoia
(H(100)-h(50))/50
so solve for h(50) and h(100) and then plug and evaluate this
dull sequoia
,w h(t) = 0.00185(250 - t)^2, solve (h(100) - h(50)) / 50
flat frigateBOT
dull sequoia
yes
flat frigateBOT
dull sequoia
i guess so
dull sequoia
did you approximate something
tidal nest
Check part b instructions
dull sequoia
i mean you did rounding
tidal nest
Yes
safe radishBOT
@tidal nest Has your question been resolved?
tidal nest
,w h(t)=0.00185(250 - t)^2, solve (h(120.001) - h(120)) / 0.001
flat frigateBOT
tidal nest
Ok
,w s(t)=4t^2 - 10t +13, solve (s(4) - s(1)) / (4- 1)
@dull sequoia
Bots not working for 3a
dull sequoia
you wrote s(t)
dull sequoia
yeah but you wrote solve h(4)
dull sequoia
where did you write to divide by 3
dull sequoia
use brackets properly
flat frigateBOT
tidal nest
,w s(t)=4t^2 - 10t +13, solve (s(1.001) - s(1)) / 0.001
flat frigateBOT
tidal nest
.close
river cobalt
Hello in my class i saw the following equation. N is a desitity function for a normal distribution, and D is a set of data (for example body height). So now is our aim to find a normal distribution N that fits our data the best. Why is it the case if we maximise this product on the right side?
safe radishBOT
Hello in my class i saw the following equation. N is a desitity function for a n...
river cobalt
is the thought right that this leads to the situation where the global maximum of this function is over the biggest cluster of data points?
safe radishBOT
@river cobalt Has your question been resolved?
river cobalt
<@&286206848099549185>
safe radishBOT
@river cobalt Has your question been resolved?
safe radishBOT
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devout linden
hello, i dont know much about Factorization, how do i Factorize with this example
x^2 + x - 12 ? pls and ty
safe radishBOT
hello, i dont know much about Factorization, how do i Factorize with this exampl...
stray socket
hello, i dont know much about Factorization, how do i Factorize with this exampl...
So a couple ways
List out positive and negative factors of -12
And then mix and match
whole acorn
x^2 + bx + c = (x + p)(x + q)
where p + q = b
p x q = c
stray socket
Or you can also do this: you know that $(x+a)(x+b) = x^2 + (a+b)x + ab$
So now you match terms:
$$x^2+(a+b)x+ab$$
$$x^2+x-12$$
Now you have a system of equations:
$$a+b = 1$$
$$ab = -12$$
flat frigateBOT
Umbraleviathan
devout linden
i found these rules, are they relevant to the question i sent? @whole acorn@stray socket
whole acorn
i found these rules, are they relevant to the question i sent? <@483962566977126...
i dont think so
your question is ax^2 + bx + c
p + q = b
p x q = ac
for 3, a is 1 btw
devout linden
i dont really understand what you sent, but the answer to what i sent is (x−3)(x+4) hower i want to know how to get there @whole acorn
whole acorn
the text on pink is the factorized equation
the black is the equation before it's factorized
safe radishBOT
@devout linden Has your question been resolved?
devout linden
im guessing you said my question was the 4th one but it doesn't match the answer to my question that i sent @whole acorn?
(x−3)(x+4)
devout linden
the text on pink is the factorized equation?
devout linden
ok, how would you factorize x^2 + x - 12 to (x−3)(x+4)
?
whole acorn
ima just reverse explain this ok?
devout linden
yes
whole acorn
try expanding (x - 3)(x + 4)
devout linden
idk how i would do it right maybe mulitplyy everything by 3 ?
devout linden
ok, x^2 + 4x - 3x - 12 ?
whole acorn
you can simplify that
devout linden
x^2 + x - 12
whole acorn
ok so now that we've proven that it's correct ima explain how i factorize it
x^2 + x - 12
list factors of -12
devout linden
idk what a common factor is
whole acorn
like..
factors of 10
5 x 2
10 x 1
common factor = 1, 2, 5, 10
just factor*
not common factor
whole acorn
negative 12 btw
devout linden
-3 x 4 or 3 x -4, -1 x 12 ?
whole acorn
there are other numbers but ok
lets just continue
p + q = 1
p x q = -12
which pair of factors when sum'd is equal to 1
devout linden
0.5 ??
whole acorn
?
whole acorn
-3 x 4 or 3 x -4, -1 x 12 ?
pair of factors from here
whole acorn
https://www.youtube.com/watch?v=9MUDAr1PnlE&t=560s
try watching this for a more detailed explanation
no need to finish it
just stop at polynomials
whole acorn
ok so
x^2 + x is
x(x + 1)
wait
oh nvm
try expanding this @devout linden
(a + b)(a + c)
devout linden
a^2+ ac + ab + bc
whole acorn
yes
whole acorn
p + q = 1
p x q = -12
now.. remember when you had to find common factors that when sum'd is equal to 1?
ac + ab will be = a
and bc = -12 : D
devout linden
we didnt find common factors?
whole acorn
yeah we found factors
my bad
a = x, b = p, c =q btw @devout linden
ok wait lets try again
expand
(x + p)(x + q)
devout linden
x^2 + xq + px + pq
whole acorn
yeah
whole acorn
p + q = 1
p x q = -12
what is p + q here?
so xq + px = x
and pq = -12
and it's x^2 + x - 12
do you understand btw
i dont think you do
im bad at explaining too
devout linden
maybe ill be back soon
whole acorn
but i wont
i gtg
soon
https://www.youtube.com/watch?v=9MUDAr1PnlE&t=560s just watch this video
it'll help
devout linden
ok when last question if you can when we factor -12 why did we have to know this
whole acorn
it doesnt have to be 1
but in this case it's 1
x^ bx + c = (x + q)(x + p)
in this case b = 1
(x + q)(x + p) = x^2 + xq + xp + pq
xq + xp makes x
cuz p + q = 1
strange quest
I'm relatively new to doing proofs, and I'm struggling to understand what is sufficient proof for something. For example, this is a pretty easy proof. I have two main questions about it though: First, is it asking me to prove that both a or v can be 0, or is it asking me to prove that at least one of them must be 0? Second, is it enough to say that we know that for all a in F, a*0=0 , and for all v in V, 0v=0, or do I need more than that?
safe radishBOT
I'm relatively new to doing proofs, and I'm struggling to understand what is suf...
strange quest
This is a solution online, which makes sense to me, but I don't know if I actually need this much
safe radishBOT
@strange quest Has your question been resolved?
safe radishBOT
@strange quest Has your question been resolved?
strange quest
Here's another example
This is obviously true because there would be no 0 vector unless b=0
but I don't really know how to put that into math instead of words
Like how to actually prove it
plucky elk
use the definition of subspace
flat frigateBOT
SilverTongue
austere spade
I think by definition of a subspace, they mean use the governing rules, like does it have an additive identity, etc
By showing those are satisfied (and that they're not when b != 0), it's been proved
Also good book, I'm reading it at the moment
strange quest
Also good book, I'm reading it at the moment
Yeah I just started going through it, its great so far
a little bit tough learning some of this stuff alone without many ways to check my work lol
austere spade
Yeah I wasn't expecting it to have no answers, a bit annoying
strange quest
My question though is like
intuitively I can see that when isnt 0, there is no 0 vector in the subspace
but i dont get how to prove that
can I literally just plug it in and say it would be
(0,0,b,0)
and thats the proof?
cause theres no additive identity thats the issue
austere spade
Can't find an actual solution online, but yeah that's what I did, that's all you'd need to write
Just that if x_4 = 0, then x_3 = b
then show that removes the additive identity
austere spade
Just finished chapter 1 lol, exam season is keeping me busy
Stopped about a month ago
strange quest
If you want I can add you and we can ask each other questions and work together through some parts lol
if not its cool
strange quest
Stopped about a month ago
ah rip gl on exams
austere spade
Tyty
austere spade
If you want I can add you and we can ask each other questions and work together ...
That'd be sick yeah, gives me a reason to get back into it
strange quest
ok great
strange quest
.close
safe radishBOT
safe radishBOT
Available help channel!
vagrant sand
You bid for a coin. You're confident that the price of the coin is between 0 and 100, if your bid is greater than the price, you win and sell it to your friend at the price of 1.5 times price. what's your bid to max your profit?
safe radishBOT
```You bid for a coin. You're confident that the price of the coin is between 0 ...
vagrant sand
anyone wanna help me with this?
solar hazel
hmm I'm confused, do you buy the coin if you win? and if so, does it cost the price, or what you bid?
ok you must buy it otherwise you would just bid 100 always
potent roost
tf is that, why don't you just bid 100 always
solar hazel
and if it costs the premade price then there is also no decision
so I think you must spend whatever you bid
light shoal
"if your bid is greater than the price, you win and sell it to your friend at the price of 1.5 times price"
is "price" referring to the same number in all three occurrences in this sentence?
as opposed to "bid", the amount you pay?
potent roost
yeah I think that too
cuz that makes the most sense
you win the bid
and get the coin
with the price you bid
solar hazel
the price you sell it at is 1.5 times the pretermined price though?
light shoal
that was what I meant by my question, does "price" refer to the unknown actual value or to the amount you pay
solar hazel
I think price is the same everywhere there
light shoal
that makes somewhat more sense, leaving aside the question of how you discover the actual value after bidding but it's unknown before bidding 😁
safe radishBOT
@vagrant sand Has your question been resolved?
vagrant sand
the question is absurd then
how
solar hazel
so umm if you bid $N$ (where $N>1$) is the expected profit $\left(\sum_{k=0}^{N-1}\frac{1.5k}{101}\right)-N$?
vagrant sand
thats the formula
solar hazel
did you get the same thing?
solar hazel
ok so let's say we bid 4
light shoal
so umm if you bid $N$ (where $N>1$) is the expected profit $\left(\sum_{k=0}^{N-...
should that N in the summand be k instead?
k is the actual value of the coin?
solar hazel
yep, oops
flat frigateBOT
Spring
light shoal
I agree with that formula
solar hazel
ok so let's say we bid 4
there is a
1/101 chance the coin value is 0,
1/101 chance it's 1,
1/101 chance it's 2,
1/101 chance it's 3,
1/101 chance it's 4,
and so on
in the case the value is 0, we win 0, if it's 1 we win 1.5, if it's 2 we win 1.5*2, if it's 3 we win 1.5*3, and if it's anything else we win 0
so the expected gain from selling the coin is 0 + (1/101)*1.5 + (1/101)*3 + (1/101)*4.5 + 0 + 0 + ... + 0
and the expected profit is that - 4 since we spend 4 to bid
@vagrant sand does that make any sense?
oh also I'm assuming between 0 and 100 to mean including 0 and 100
safe radishBOT
@vagrant sand Has your question been resolved?
peak whale
Can this turn into b = 64/a and if so, how does it happen?
safe radishBOT
Can this turn into b = 64/a and if so, how does it happen?
primal kelp
yes
so you wanna make the b the variable
so you wanna get rid of the 8 on the bottom of b
so you times it by itself by 8, and whether you do that, you always have to times whatever you're timesing to the other side too
so it would be 8/a(8) = b
because of 8*8, they cancel out which only give you b on the right side
8*8 = 64 therefore 64/a = b
primal kelp
np
rancid wagon
Can this turn into b = 64/a and if so, how does it happen?
64 = ab , b = 64/a
hybrid wren
