A and all not A
#help-0
royal plank
no
lucid depot
then i neglected the u
lucid depot
is that on the left?
royal plank
yes
lucid depot
oh
royal plank
left the line right after
lucid depot
but that's not a union complement a
that's a union a
i have not once wrote a complement there
lucid depot
btw if you find explaining it complicated we can hop into voice chat and you lead me through the solution
if that's ok with you
royal plank
no, i have no mic here
royal plank
if you can solve it and compare your solution with mine
you'd need de morgans Laws to prove that, so I did it visually
lucid depot
picture is loading
quartz cave
If I get all the successors of a given variable in a probability graph
quartz cave
Do I then have all variables that contain that parent variable in their conditional probability table?
It cannot appear anywhere else right?
lone heartBOT
@quartz cave Has your question been resolved?
blazing grail
What is this task?
lone heartBOT
What is this task?
royal plank
What is this task?
do you know the euler torrient function?
that funny symbol before (k)
blazing grail
do you know the euler torrient function?
Ah yeah, that might be it. actually funny that we've been using slighlty different notation for euler in handwriting 😄
royal plank
Ah yeah, that might be it. actually funny that we've been using slighlty differe...
yeah, a lot of handwritten and computed greek symbols look different, but this is the euler torrient function
you need any help on that or do you know what to do now?
blazing grail
I think I can manage it, haven't started yet as I didn't know what this was, but thanks!
.close
dull phoenix
I set the X on my calculator to -10000 but I want the X to represent the variable X when putting it into a function since I want to write X as an exponent (^X). How do I turn X = -10000 to X = a normal X?
dull phoenix
Calculator TI-84
noble sinew
Don’t set X=-10000 then?
If you are asking how to revert that for example just system reset or whatever it is called
dull phoenix
I did but nothing changed
dull phoenix
Don’t set X=-10000 then?
I want to get back to the normal X
dull phoenix
okey now it worked, I had to clear the memory of the calculator but it just set X = 0
which isn't optimal
I'll just google
noble sinew
Google can answer most questions and should really be a 1st step
sharp peak
the drawing shows a sketch of the graph of the function f(x)= ln(ax)/x. g(x)= -ln(ax)/x, when a > 1. Pass a straight line through the extreme points of the two functions f(x),g(x). the area bounded by the straight line, by the graphs of the two functions and by the line x = e, equals to (ln(2e))^2 -1. find the equation of the line that passes through the point of inflection of f(x) and through the inflection point of g(x). please help whoever's got free tim
woeful pulsar
have your drawn the area?
woeful pulsar
hmm so inflection point is when second derivative is 0
sharp peak
im struggling to find the area
woeful pulsar
can you write it as an integral?
lone heartBOT
@sharp peak Has your question been resolved?
marble prawn
lone heartBOT
marble prawn
plz help
woeful pulsar
do you remember what nabla^2 is
woeful pulsar
yeah, but do you recall the definition of nabla^2
marble prawn
yeah i know that, its not that easy
woeful pulsar
what have you tried so far
light flame
Hey guys, you can say anything about me but pls let me help with my math I don't really get it.. I'm a slow learner
light flame
I failed dnd I don't wanna fail this time again
lucid socket
obtuse mango
yoo stop bullying 🙂
light flame
This is the question
light flame
R u in the wrong Channel
lucid socket
R u in the wrong Channel
I'm new i don't know 💀
light flame
Okay
obtuse mango
and 2x-y=3 as 2nd equation
light flame
So I'm gonna answer the first equation
obtuse mango
so u can see that x and y is squared in equation 1 right?
so square all the numbers on the 2nd equation to get x^2 and y^2
light flame
so u can see that x and y is squared in equation 1 right?
Yes
light flame
Ok hold on
light flame
I have solve that actually but it different
light flame
ok so
void solar
You guys got this?
obtuse mango
You guys got this?
oui oui monsieur
void solar
light flame
So first I solve the equation for y
light flame
And move the variable to the right handed side and change its sign
obtuse mango
And move the variable to the right handed side and change its sign
ahh right
void solar
could you please get me some help at <#903430333096132618> ?
Yeah sorry I haven’t seen ordered pairs so idk what they are
obtuse mango
Yeah sorry I haven’t seen ordered pairs so idk what they are
ahh all g mate
obtuse mango
oh ok cool!
light flame
y = - 3 + 2 x
obtuse mango
ahh nice
i actually did that once but I got marked down 😦
so I had to do the square method instead
light flame
And then substitute the given value of y into the equation
obtuse mango
And then substitute the given value of y into the equation
yep easy m8
obtuse mango
And then substitute the given value of y into the equation
out of curiosity what year/grade r u?
light flame
8
light flame
So it x^2 + ( - 3 + 2x)^2 = 27
obtuse mango
xD
light flame
Am I right
obtuse mango
Am I right
yeah thats right
void solar
bruh im in 11
In Aus?
void solar
Finished yr12 vce
obtuse mango
Finished yr12 vce
oh so vic?
void solar
Yep
light flame
yeah thats right
And I'm 15yo but I failed so I came back to 8
obtuse mango
oh cool! from west aus ahaha
obtuse mango
And I'm 15yo but I failed so I came back to 8
bro thats sad man
obtuse mango
And I'm 15yo but I failed so I came back to 8
😭😭
void solar
And I'm 15yo but I failed so I came back to 8
As long as you keep trying
obtuse mango
And I'm 15yo but I failed so I came back to 8
you'll achieve your goals and dreams
obtuse mango
And I'm 15yo but I failed so I came back to 8
keep it up
obtuse mango
I'm confused on the next part
oh sorry
so for this you have to expand (-3+2x)^2
have u learnt factorising polynomials
light flame
I'm confused but what I first did
obtuse mango
about>
light flame
have u learnt factorising polynomials
Ye I did but the teacher isn't understandable
light flame
oh it fine
obtuse mango
I have to go
obtuse mango
oh it fine
really sorry!
cya
hope u get help with ur question
Or search up an app called Photomath
dont use it all the time though
use it to check ur answers
it has all the steps
peace man
light flame
Or search up an app called Photomath
I'm on PC
lone heartBOT
@light flame Has your question been resolved?
viscid silo
a . b . c are real number no nul whit ab +ac + bc = 0
Show that a+b/c + a+c/b + b+c/a =-3
slender gull
Do you mean (a+b)/c + (a+c)/b + (b+c)/a
viscid silo
Yeah
slender gull
So to add these you have to take LCM.
slender gull
And?
If you've already attempted something, why would you not show your attempt first thing?
viscid silo
But i didn't continue
alpine sable
why not
gray isle
doesn't matter
viscid silo
If you've already attempted something, why would you not show your attempt first...
I get the lcm but i think the factorization is false
scenic socket
Hello! I'm not sure exactly if I should be answer part a) with a hypothesis/conclusion format or simply a formalized format.. Also for part b) I am totally lost on how to prove this
lone heartBOT
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lone heartBOT
lone heartBOT
Available help channel!
boreal verge
hey can anyone check my work cause this was kinda confusing and im not sure i did it right
lone heartBOT
hey can anyone check my work cause this was kinda confusing and im not sure i di...
boreal verge
oh right l
forgot i had that one open
if x is 0 it would just be $1 + 2 + 3 + ... + n \ge 59 => \frac{0(0-1)}{2}+\frac{n(n+1)}{2} \ge 59
=> (n)(n+1)\ge 118 =>n²+n \ge 118\\vdot\
\vdot\
\vdot\$
if x is 2, it would mean $|2-1|+|2
-2|+|2-3|+...+|2-n| = 1 + 0 + 1 + 2 + 3 + ... + |3-n| = \frac{2(2-1)}{2} + \frac{|3-n|(|3-n|+1)}{2}\
\vdot\
\vdot\
\vdot\$
for a general scenario, it could be interpreted as 2 sums, one of x-1 terms and one of n-x+1 terms (the +1 being the case where x = n)
therefore, a general formula would be:
$|x-1|+|x-2|+...+|x-n| = \frac{x(x-1)}{2} + \frac{|x-n|(|x-n|+2)}{2}=\frac{x(x-1)+|x-n|(|x-n|+1)}{2}$
i wanted to rewrite the sum |x-1|+|x-2|+...+|x-n|, where x is any real number and n is any natural number
tried induction and noticing some things in regards to how the sum behaves when x increases
and i assume it applies when x is decreasing as well
its just that with a minus in front
ocean sealBOT
Kel.plush
hollow lodge
The steps you have taken to derive a formula are generally correct, but there are a few errors in the final formula you have given. The formula you have given is not correct because the first term of the sum, $|x-1|$, is not being included in the formula. Also, the second term of the formula, which should represent the sum of the remaining terms, is not correct.
The correct formula for the sum of the absolute values of the numbers from $1$ to $n$, where $x$ is an integer between $1$ and $n$, should be as follows:
$|x-1| + |x-2| + |x-3| + ... + |x-n| = |x-1| + \frac{(n-x)(n-x+1)}{2}$
This formula is derived as follows:
The sum of the absolute values of the numbers from $1$ to $n$ can be split into two parts: the sum of the absolute values of the numbers from $1$ to $x-1$, and the sum of the absolute values of the numbers from $x$ to $n$. The first part is simply equal to $|x-1|$ because the absolute value of a positive integer is just the integer itself. The second part is a bit more complicated, but can be derived as follows:
$|x-1| + |x-2| + |x-3| + ... + |x-n| = |x-1| + (|x-n| + |x-(n-1)| + |x-(n-2)| + ... + |x-1|)$
We can rewrite the second part of the sum as follows:
$|x-1| + (|x-n| + |x-(n-1)| + |x-(n-2)| + ... + |x-1|) = |x-1| + (|x-n| + |n-x| + |n-1-x| + ... + |1-x|)$
Now, we can see that the sum of the absolute values of the numbers from $x$ to $n$ is simply the sum of the integers from $1$ to $n-x$, which is equal to $\frac{(n-x)(n-x+1)}{2}$. Therefore, the final formula for the sum of the absolute values of the numbers from $1$ to $n$ is as follows:
$|x-1| + |x-2| + |x-3| + ... + |x-n| = |x-1| + \frac{(n-x)(n-x+1)}{2}$
ocean sealBOT
MeatBagFrank
hollow lodge
np bro
lone heartBOT
@boreal verge Has your question been resolved?
void canyon
lone heartBOT
iron widget
your answer true
iron widget
7 units down
last ether
It's just finding the change in x and change in y
void canyon
like 90% sure
last ether
Is this homework
iron widget
@void canyon if your x coordinates increase or decrease you can go left or right
y coordinates increase or decrease you can go up or down
void canyon
Is this homework
yeha on saturday
void canyon
y coordinates **increase** or **decrease** you can go **up** or **down**
thats good to know im writing this down right now
iron widget
true
void canyon
last one
iron widget
true
alpine sable
lone heartBOT
@void canyon Has your question been resolved?
shell cloak
Hey there,
I'm currently trying to figure out how to do a Progressive Calculation in Context of the Etsy Marketplace. The goal is to be able to easily calculate for what price I need to list a product to be profitable.
However, Etsy calculates their fees in a very cross-linked way, so it is grilling my brain right now. Due to the cross-linking, I don't even know whether it's possible, but you can prove me wrong ^^
The Retrograde Calculation has worked fine (See right side of the sheet).
Note, this isn't the entire calculation, but the relevant part, for this question
Note, I've marked all base values with the purple arrows (e.g. The base value of VAT is Net Etsy Selling Price)
Retrograde Calculation: $9,98 -> ?Selling Price
Progressive Calculation: $5,88 -> ?Gross Etsy Selling Price
cheers
ocean sealBOT
BennoDev
Hey there,
I'm currently trying to figure out how to do a **Progressive Calculation** in Context of the Etsy Marketplace. The goal is to be able to easily calculate for what price I need to list a product to be profitable.
However, Etsy calculates their fees in a very cross-linked way, so it is grilling my brain right now. Due to the cross-linking, I don't even know whether it's possible, but you can prove me wrong ^^
The Retrograde Calculation has worked fine (See right side of the sheet).
**Note**, this isn't the entire calculation, but the relevant part, for this question
**Note**, I've marked all base values with the purple arrows (e.g. The base value of `VAT` is `Net Etsy Selling Price`)
**Retrograde Calculation:** `$9,98` -> `?Selling Price`
**Progressive Calculation:** `$5,88` -> `?Gross Etsy Selling Price`
cheers
lone heartBOT
@shell cloak Has your question been resolved?
lone heartBOT
@shell cloak Has your question been resolved?
fluid flame
lone heartBOT
fluid flame
Hi i need help making a curved line for this
best i could do was y = 1000x^-1
or 1000/x = y
peak python
last ether
last ether
What do they look like
Wait it follows a very distinct pattern
Lol each y value gets halved
That's just 2000(0.5)^x
last ether
$$A_0(r)^x$$
$A_0$ is the initial, (when $x = 0$), and then $r$ is the rate
ocean sealBOT
Umbraleviathan
last ether
Np
peak python
peak python
bro it aint showing one
last ether
There's legit 3 available
lone heartBOT
fluid flame
Thanks again!
lone heartBOT
Available help channel!
snow orchid
elfin tendon
i think you just need to find the first derivative like you did and substitude x for -2 or f`(x)= 2
lone heartBOT
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alpine sable
how do you use partial fraction decompositon
lone heartBOT
how do you use partial fraction decompositon
echo socket
Did you mean to write x instead of t?
alpine sable
Did you mean to write x instead of t?
oh yea ye sorry
echo socket
Factor the polynomial in the denominator by first noticing that x = 1 is one of its roots
After doing long division you should be able to discover that x = 1 is actually a double root, making the polynomial eventually equal to (x - 1)^2(x^2 - x + 1)
alpine sable
After doing long division you should be able to discover that x = 1 is actually ...
im sorry but im bad at maths and i dont know how to factorise
echo socket
Do you know how to do long/polynomial division?
echo socket
Try dividing x^4 - 3x^3 + 4x^2 - 3x + 1 by x - 1
echo socket
1 - x = -(x - 1)
Dividing 1 - x by x - 1 yields -1
So, did you get x^3 - 2x^2 + 2x - 1 as the quotient?
alpine sable
yess
echo socket
And, clearly, x^3 - 2x^2 + 2x - 1 has a root at x = 1
Meaning you have to divide by x - 1 again
echo socket
Guess and check, usually I try out x = -1 and x = 1
If those don't work, try x = -2 and x = 2
But I don't go further than that most of the times
alpine sable
ohhh
echo socket
Or, if the coefficients of the polynomials are all integers, you may wanna look at the rational root theorem
echo socket
Did you get x^2 - x + 1?
Alright, x^2 - x + 1 actually has no roots so the factoring is done
x^4 - 3x^3 + 4x^2 - 3x + 1 = (x - 1)^2(x^2 - x + 1)
(x - 1)^2 is squared because we got x = 1 to be the root twice
echo socket
If x = a is a root of polynomial P(x), then (x - a) is a factor of P(x)
So P(x) is divisible by that
alpine sable
ahhh
alpine sable
x^4 - 3x^3 + 4x^2 - 3x + 1 = (x - 1)^2(x^2 - x + 1)
and for this part, we take the last quotient to equate and possible roots?
can you help me undestand why it got written as such?
we have the root, but how did it got subtracted
<@&286206848099549185>
hazy cloak
if you try to go backwards, ie cross multiply and subtract you will see you are getting your previous line
like 1/n(n-1) = (n+1-n)/n(n-1) = 1/(n-1) - 1/n
alpine sable
like 1/n(n-1) = (n+1-n)/n(n-1) = 1/(n-1) - 1/n
how can you write (n+1-n)/n(n-1) = 1/(n-1) - 1/n ?
hazy cloak
look at the numerator, it is 1, you can write 1 as 1+n-n
hazy cloak
yess
alpine sable
ahh thanksss!!
hazy cloak
let me try and write it down
alpine sable
oh wait i got it, add aand subtract (x-1)^2
expand (x-1)^2+x and it doesnequate to that
thanks alott man
hazy cloak
i wrote it very roughly i hope you understand
hazy cloak
expand (x-1)^2+x and it doesnequate to that
yes exactly
hot delta
lone heartBOT
golden geyser
this is matrix/eigenvalues?
abstract fractal
I would double check how you distributed
hot delta
thx
lone heartBOT
Available help channel!
opal imp
ok so i'm doing a math assignment due on November 12th on mortgage and finance where i am given a scenario about buying a house and have to do payment calculations using a TVM solver. i need to know which is the best interest rate from each mortgage term as well. If someone can help me and check out the assignment i would greatly appreciate it
vital sail
ok so i'm doing a math assignment due on November 12th on mortgage and finance w...
To determine which is the best interest rate from each mortgage term, you will need to consider a few factors, such as the total cost of the loan, the monthly payment amount, and the length of the loan term. You can use a TVM solver, which is a tool that allows you to input different values for the interest rate, loan amount, and loan term, and then compute the monthly payment and total cost of the loan. By comparing the results for different interest rates, you can determine which rate offers the best combination of monthly payment and total cost for your specific situation.
opal imp
To determine which is the best interest rate from each mortgage term, you will n...
I don't see any loan info here
jus the price of the house and the downpayment
with different interest rates for a fixed-rate mortgage (for 1, 2 and 5 years) and i gotta find out which one is the best from each
3 different banks too
it's confusing 😭
@vital sail
lone heartBOT
@opal imp Has your question been resolved?
lone heartBOT
@opal imp Has your question been resolved?
lone heartBOT
@opal imp Has your question been resolved?
abstract sorrel
If there are 5 different candies in a jar and a child wants to take out one or more candies, in how many ways can this be done?
Combination
quiet blade
I solved this problem but I'm not sure if I did the bounds correctly. I assumed since you need to make the bounds with respect to z, y, and x, I would just set them to 0 but I'm not sure if that is a correct assumption.
lone heartBOT
I solved this problem but I'm not sure if I did the bounds correctly. I assumed ...
@quiet blade Has your question been resolved?
primal galleon
lone heartBOT
primal galleon
how do they get 1<x<2?
primal galleon
why (x-1)(x-2)(x+1)
isn't it (x-1)(x-2)
the numerator is (x-1)(x-2)
and denominator (x-1)
plain flame
its because negative times positive is negative
primal galleon
$$\frac{x^{2}-3x+2}{x+1} <0\Leftrightarrow \left( x^{2}-3x+2<0\ \wedge x+1>0\right)$$
$$\vee \left( x^{2}-3x+2>0\ \wedge \ x+1<0\right)$$
$$\Leftrightarrow \left( x^{2}-x-2x+2<0 \wedge \ x>-1\right)$$
$$\vee \left( x^{2}-x-2x+2>0\ \wedge \ x<-1\right)$$
This is my understanding so far.
$$x^{2}-x-2x+2\Leftrightarrow x\left( x-1\right) -2\left( x-1\right) \Leftrightarrow \left( x-2\right) \left( x-1\right)$$
primal galleon
But how do you turn (x-2)(x-1) to 1<x<2?
gray isle
consider the graph of y= (x-1)(x-2)
a rough sketch with x-intercepts and correct concavity is sufficient
primal galleon
,w graph (x-1)(x-2)
ocean sealBOT
primal galleon
i don't have access to a graphing calculator on the exam
gray isle
don't need one
primal galleon
so i write (x-1)(x-2) = 0
gray isle
a rough sketch with x-intercepts and correct concavity is sufficient
primal galleon
find the x-intercepts
wanton tusk
the shaded area
primal galleon
how do we know it's a third degree polynomial
wanton tusk
we have 3 x’s multiplied
primal galleon
how
gray isle
you can multiply both sides by (x+1)^2, (a non-negative value) which leads to the third line
wanton tusk
yepp
gray isle
the work just posted was more efficient approach
the question you were initially asking is very similar
your quadratic
(x-1)(x-2)
is in factored form, you should have no issue identifying the zeros
and concavity
i don't have access to a graphing calculator on the exam
don't need one
a rough sketch with x-intercepts and correct concavity is sufficient
your sketch could be as horrid and bare bones like
primal galleon
the zeros won't change if it's <0, >0, or =0 right?
gray isle
and from that very rough sketch
you should be able to see when the curve is less than zero and when its greater than 0
primal galleon
so the area of the curve under the abscissa is when (x-1)(x-2) < 0?
gray isle
whut
primal galleon
the x-axis
gray isle
what's this about area
lone heartBOT
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fast shell
hi
fast shell
in Applied Optimization whats the difference between the objective and the constraint
lone heartBOT
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lone heartBOT
@fast shell Has your question been resolved?
lone heartBOT
@fast shell Has your question been resolved?
gusty gorge
in Applied Optimization whats the difference between the objective and the const...
objective is what you want to maximize / minimize, constraint is what the things have to satisfy
lone heartBOT
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lone heartBOT
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mellow grail
Construct a sector AOB with angle AOB equal to 45 deg. Now, create an angle bisector that bisects AOB and the arc AB. Finally, extrude the bisector to point C, so that OC = 20 units. Then construct a semi-circular arc ACB. Find ACB, and the arms of the sector OA and OB
lone heartBOT
Construct a sector AOB with angle AOB equal to 45 deg. Now, create an angle bise...
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lone heartBOT
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alpine sable
Please help to calculate the Fourier transform of the function f(x) = sin(2π10x)
naive valley
i assume you're meant to do this in terms of dirac deltas?
alpine sable
i assume you're meant to do this in terms of dirac deltas?
UPD: yes
alpine sable
no
naive valley
what fourier transforms do you know?
lone heartBOT
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alpine sable
.close
gaunt depot
A math olympiad problem, i got problems with
lone heartBOT
A math olympiad problem, i got problems with
gaunt depot
i tried to do this by using tan as a a,b,c
and it seems working but i cant progress i dunno why
Udowodnij że means- prove
alpine sable
how do you find what part is 225 of 2000
lone heartBOT
@gaunt depot Has your question been resolved?
gaunt depot
how do you find what part is 225 of 2000
by dividing
alpine sable
how do you find what part is 225 of 2000
divide 225 by 2000
lone heartBOT
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dim temple
hi
lone heartBOT
@gaunt depot Has your question been resolved?
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Available help channel!
forest coyote
lone heartBOT
alpine sable
We cannot give you the answer. But we can help/guide you to it
forest coyote
yup that will do
alpine sable
<@&286206848099549185>
Also please do not ping the helpers role until at least 15 minutes after your question has been up
forest coyote
ohh sorry im just in a hurry beacause i still have to review😓
alpine sable
Well, we can start with the first one. The domain describes the input values (the x's) for the function, do you know how to discern the x values for a function from its graph?
alpine sable
ohh sorry im just in a hurry beacause i still have to review😓
thats fine
forest coyote
Well, we can start with the first one. The domain describes the input values (th...
uhmm not yet cuz this is an activity and im in modular so self learning sorry
alpine sable
yeah thats okay
lets start off with the first dot
Do you see that horizontal axis in the middle labelled as 'x' in the far right? @forest coyote
forest coyote
Do you see that horizontal axis in the middle labelled as 'x' in the far right? ...
yes
alpine sable
That's called the x-axis and it tells you the values of your x values, the labelled numbers on that axis are those values
forest coyote
That's called the **x-axis** and it tells you the values of your x values, the l...
ohhh
alpine sable
x = -2, for example would be this point
we are speaking strictly one dimensionally here though, so ignore the vertical axis for now
forest coyote
okay following🤍
alpine sable
alright, so do you see all of those black dots?
forest coyote
yes
alpine sable
i want you to look at them and look at the correspondent x value of that point
so for example
forest coyote
-3 -2?
alpine sable
this black dot is at the point x = 2 (again we are only concerned with the x values for now)
forest coyote
ohh okay🤩
alpine sable
can u tell me where all of the rest lie?
forest coyote
-3 -2 -1 0 1 2 3
alpine sable
yep! you are doing amazing good job
okay, so those x values you just listed down are what we call the domain of the function
think of the domain as, ALL of the x values on that graph
if that makes sense
so your domain of that function would be the x values of -3, -2, -1, 0, 1, 2, 3
please tell me if u r confused at all at any point btw
is it alright so far?
forest coyote
okay, so those x values you just listed down are what we call the **domain** of ...
or the abscissa right?
forest coyote
is it alright so far?
yep!!
alpine sable
or the abscissa right?
hmm i think abscissa is like, the general term for any x values, not necessarily the domain of the function
but i am unsure because i dont think i have used that term in a long time 😅
forest coyote
hmm i think abscissa is like, the general term for any x values, not necessarily...
ohhh thanked god i got corrected cuz i might put the wrong answer on our quiz
alpine sable
ohhh thanked god i got corrected cuz i might put the wrong answer on our quiz
mhm the domain of a function is always safer, if you are trying to describe all the x values for a function
okay so like, here is where i need your help a bit
forest coyote
owkey!
alpine sable
i need to ask from you how exactly would you write a set or domain, if you were asked to write down one
if you dont know thats fine, but then we kinda have to talk about something else for a bit
alpine sable
yep! that sounds good to me
good job, thats ur domain of the function
now, lets talk about the range
forest coyote
ohhh well i thought it was going to be hard😅
alpine sable
Nope! u already got it hahaa
now, we have to find the range
u see what we did with teh domain and the x values? well we are going to do the same exact thing
but now, we are doing it for that vertical line, thats called the y-axis
is this okay with u so far? @forest coyote
forest coyote
yesss!!
alpine sable
okay! thats great
Okay, so the domain describes the x values or the "inputs" of that function
the range describes the y values or the "outputs" of that function
it goes like this, think of it
x -----> function -----> y
the function is just this like, fancy machine, that converts your x to a y, if that makes sense
well anyways
forest coyote
the function is just this like, fancy machine, that converts your x to a y, if t...
ohhhhh
alpine sable
for the graph, this point would have y = 1
for example
you see how it is x = -3, and y = 1 at the same time?
forest coyote
okay then it is the range?
forest coyote
so basically if the set is (-3, 1) (-2,-1) the domain is -3 and -2 then the range is 1 and -1?
forest coyote
ohhhh
alpine sable
but thats a very small function haha, functions usually are huge and go on forever, and we are going to see that in a bit
alpine sable
for the graph, this point would have y = 1
but for now, can u tell me the range for this?
like, just list off the y values
for the points
forest coyote
for the graph, this point would have y = 1
1, -1, -2, -1, 2, 0?
alpine sable
yep!! you are actually doing fantastic, good job
okay so here is the thing, actually
forest coyote
yep!! you are actually doing fantastic, good job
thank you!
alpine sable
in sets (if you dont know what that is, just think of the domain and range for now) repeated numbers don't matter
like
you wrote down -1 twice right? because it appeared twice right?
actually u can just write down a single -1
forest coyote
actually u can just write down a single -1
ohhhh i see
alpine sable
yep! but can u write out the range properly now?
like how u did with the domain earlier
forest coyote
{(1, -1, -2, 2, 0)}
forest coyote
yey!
forest coyote
now we can move on for the second question
yay!!
alpine sable
okay before we get into the second question, i want to mention a few important things first
do you notice how we have arrows at the red parts, but just a dot at the yellow part?
do you know the difference between the arrow and the dot?
forest coyote
do you know the difference between the arrow and the dot?
uhmm not yet?
alpine sable
mm alrightyy
so basically, there are three types of lines
one is called a segmented line, the second a ray, and the third just a "line" actually haha
forest coyote
one is called a segmented line, the second a ray, and the third just a "line" ac...
so the first one is line the other one is segmented? (just a guess)
alpine sable
alpine sable
so the first one is line the other one is segmented? (just a guess)
you are right for the first!
alpine sable
i drew this quickly, but let me explain the difference
forest coyote
you are right for the first!
ohhh just observation based on the names hehe
alpine sable
ohhh just observation based on the names hehe
haha thats great! it is good to be observant :))
alpine sable
a "line segment" is actually probably what you refer to as a "line" normally in your mind
a line segment is just a line from like one point to another
it has a specific length
like 4, 5, 6 whatever it may be! but we know how long it is
forest coyote
ohhh
alpine sable
thats the reason it begins with a dot and ends with a dot
it has like a starting point and an end point
forest coyote
ohhhhhhh that makes sense
alpine sable
now, with a ray, things are a bit different
we have a "Start" point
but like, if u notice, at the end we have an arrow instead of a point like we did with a line segment
the little "Arrow" actually means that the line...continues on forever!
it has a starting point, but it never stops
forest coyote
the little "Arrow" actually means that the line...continues on forever!
ohhhh but the dot means the end??
alpine sable
ohhhh but the dot means the end??
yep! the dot basically means the start or the end point
like we had with a line segment
forest coyote
yep! the dot basically means the start or the end point
ohhh im starting to gets things now
alpine sable
like u can continue drawing it forever in the direction where it is heading
forest coyote
like u can continue drawing it forever in the direction where it is heading
an infinite line
alpine sable
yep!
like here
i exteded it a bit, but it really does just go on forever
in the direction that it is shown
forest coyote
ohhh i see i get it
alpine sable
yep!
okay here is the thing, thats all fine and dandy, but now for the "line"
it is kind of like the same story as a ray, buuuuut, it actually doesnt begin anywhere either
forest coyote
an infinite line then
alpine sable
it doesnt have a beginning point neither does it have an end point like we had with a line segment
yep!
to illustrate
(the lines need to be straight, but my art skills are just not that great ahaha)
is the idea fine by you tho btw?
forest coyote
to illustrate
it's a straaight line though
forest coyote
is the idea fine by you tho btw?
yessss
alpine sable
yeahh i am just bad at drawing
ahahaha
okay so actually, the arrow and dot stuff isn't just for lines
if you see like anything on a graph right? and u see it has some end with an arrow, just realise that it goes on forever after that point
forest coyote
but im still confused how to get the range having an infinite line🤔
alpine sable
we will get into that!
to illustrate what i meant earlier, here for example, the orange line is just a simple line that goes to infinity like i told u
the yellow weird thing, if you notice, has yellow arrows at its end too
those arrows basically mean that it continues to grow forever and forever and forever in those directions
forest coyote
the yellow weird thing, if you notice, has yellow arrows at its end too
so its infinite too??
alpine sable
yep!
u got it
it goes to infinity
to where the arrows are heading
okay so knowing this, lets head into question 2
forest coyote
ohh okayy!!
alpine sable
forest coyote
getting exciting!!
alpine sable
okay so like, off the bat, we can realise that the thing is going to infinity right
because of the arrows
it is a line that goes left and right to infinity and forever and forever
okay so here is the tricky part! finding the domain and range here is going to be a bit more interesting for us
lets find the domain first
you can ignore the y values for now, i want you to just look at the x values
like we already talked about you knoww
what do u guess the domain is?
forest coyote
probably 0??
alpine sable
not quite! lets think this through a bit more
this line continues going on forever right?
forest coyote
this line continues going on forever right?
yes
alpine sable
i want you to look at it on the right, and imagine if it continued going right and right and right
it would reach x = 20, x = 100, x = 1000, x = 10000
and larger and larger numbers
forest coyote
yep!
alpine sable
yep!
okay so the domain tells us the x values that the function has
so if we know that it continues going forever and forever from both sides
it can be -10000, -1000, 0, 1000, 100000 and so on
if it can have ANY x value, like we can see, what do u think the domain would be?
forest coyote
if it can have ANY x value, like we can see, what do u think the domain would be...
ohhh anything?!
alpine sable
yes!!
the domain is anything!
but..."Anything" isnt quite...the right word
if like you wanted to say that the function goes on to forever, we can just say it goes to infinity
okay so here is another thing, i need to know, if i told you the phrase "All Real numbers" would you know what i mean by that?
its okay if you dont
it just means, we have to go another way
forest coyote
okay so here is another thing, i need to know, if i told you the phrase "All Rea...
it include both rational and irrational numbers?
alpine sable
oh so you know of it! thats good
that makes things a bit easier
but yes, a real number is any number you can think of (outside of complex numbers but thats for the future)
A real number is ANY number
So the domain here is All real numbers
but we can rewrite it in a different way
which is this
[-\infty, \infty]
hm, bot is down?
$f$
sigh what a bad timing
forest coyote
So the domain here is **All real numbers**
ohhhh i get it!!
alpine sable
but we can rewrite it in a different way
the first one is called interval notation, and the second one...you can just call inequality notation
both of those mean all real numbers
are u familiar with either of those by any chance? @forest coyote
forest coyote
are u familiar with either of those by any chance? <@932577001242521620>
yep im kind of familiar with the notation
but wait
based on the example on our paper the domain and range is written like this any idea??
alpine sable
oh okay you guys are using set notation
can i know what year you are in?
just to figure out in which way i should give out the stuff to you
forest coyote
can i know what year you are in?
second year highschool
alpine sable
based on the example on our paper the domain and range is written like this any ...
do u know what this means
the way u wrote it
forest coyote
do u know what this means
well yes but how to get it or to be exact how to make it is confusing for me
forest coyote
aaa why did the bot break now smh
but lemme guess your a teacher?
alpine sable
well yes but how to get it or to be exact how to make it is confusing for me
hmm okay! we can explain
forest coyote
i think i am like 2-3 years older than u or something
i think you should do tutoring u might even earn money
alpine sable
i have so much to study for, it is kind of hard to multitask 😅
forest coyote
i have so much to study for, it is kind of hard to multitask 😅
oh but actually from what your doing rn explaining and everything can be paid
if i can send you money i will your very good at explaining
alpine sable
nonono please dont, i just like teaching people and I don't want any money from here
it is also nice to see people learn more stuff you know?
forest coyote
well yeah but i mean if you need money its a good sideline
forest coyote
hmm okay! we can explain
but getting the number even adding more than and less that is even harder
alpine sable
the bot is down so i cant just type stuff with it sadly, but i found this to explain
alpine sable
but getting the number even adding more than and less that is even harder<:happy...
ahahahah it is okay
u will get used to it dw
alpine sable
the bot is down so i cant just type stuff with it sadly, but i found this to exp...
the stuff ur teacher showed is basically this, when you have something of this form it is read out as "the variable x such that x is in all real numbers"
forest coyote
the stuff ur teacher showed is basically this, when you have something of this f...
ohhh
alpine sable
the fancy ∈ letter just basically means "is in"
so like x ∈ R basically means "all x is in R"
{x | x ∈ R} is ur domain for the function u had above
forest coyote
ohhhh
alpine sable
okay so thats the domain down, is there anything confusing u at all about this btw?
forest coyote
ohhh but how do we turn this thing to that??
alpine sable
ohhh but how do we turn this thing to that??
like, we already figured out the domain is all real numbers right?
forest coyote
like, we already figured out the domain is all real numbers right?
yeppp
alpine sable
set builder notation, which is what u used above, basically describes that more formally
if we were to properly write it out, it would be
D : {x | x ∈ R}, which read out basically means
"The domain of the variable x belongs to all real numbers"
if we were to write
R : {y | y ∈ R}
it would be read out as "The range of the variable y belongs to all real numbers"
and so on
if like
in our first example
forest coyote
if we were to write
R : {y | y ∈ R}
it would be read out as "The range of the ...
but the first one has domain?
alpine sable
with the points, we had the domain be {(-3, -2, -1, 0, 1, 2, 3)}
alpine sable
but the first one has domain?
oh what do u mean?
alpine sable
with the points, we had the domain be {(-3, -2, -1, 0, 1, 2, 3)}
this, we can write in set builder notation as
forest coyote
this, we can write in set builder notation as
ohh so we don;t have to turn it into like this??{x | x ∈ R}
alpine sable
mm actually
i made a mistake
set builder notation is for continuous values
roster notation is for discrete values
you have three forms to write it in
Roster notation, set builder notation, and interval notation
forest coyote
oh
alpine sable
the last two dont work for our first example
because we had ONLY the points -3,-2,-1, etc.
set builder notation,
with like -3 < x < 3 is wrong here to use, because it means the domain is all x values between -3 and 3
but we dont have something like 2.5 or 0.5 yk
we only have -3, -2, -1, 0, 1, 2, 3 and nothing inbetween
okay this is really a confusing mess for you, lets just rewind it a bit for ya
lets go back to whats confusing you, can you tell me if anything is?
alpine sable
set builder notation,
with like -3 < x < 3 is wrong here to use, because it mean...
i mean unless u define x for integer values then it would be fine, but
forest coyote
lets go back to whats confusing you, can you tell me if anything is?
YEPP!! I WILL!
alpine sable
yeah so lets recollect what we have done so far
what is the domain of our function?
oh btw if you are tired, or busy, or this is maybe taking too long for you, we can continue this conversation later if u wanna
forest coyote
oh btw if you are tired, or busy, or this is maybe taking too long for you, we c...
uhmm im busy but i have to pass this assignment tommorrow so im kind of in a rash
im doing 3 other subjects rn HEHEHHE
alpine sable
uhmm im busy but i have to pass this assignment tommorrow so im kind of in a ras...
mm thats okay, we can finish this quickly hopefully
alpine sable
im doing 3 other subjects rn HEHEHHE
oh WOW
thats a lot of multitasking ahaha
maybe we can continue this later then after u finish off the other two? its easier on u as well
forest coyote
maybe we can continue this later then after u finish off the other two? its easi...
umm i can do that but i have to atleast sleep at 3am cuz i have to wake up at 8am
alpine sable
oof whats the time for u?
forest coyote
oof whats the time for u?
12:30am
alpine sable
oh yeah u do have to speedrun this then ig
forest coyote
oh yeah u do have to speedrun this then ig
yahh i have to be flash😆
i'll also try to answer it but i'll be back for the explanation about 2:00am i guess
forest coyote
i will be up i think
ohh okayy🤍
alpine sable
i'll also try to answer it but i'll be back for the explanation about 2:00am i g...
try to read your notes on how to construct with set builder notation, and for the rest of the graph questions, do the same thing of examining the x and y values for the domain and range respectively
for your last two questions on that list without a graph
i need you to realise that f(x) = x - 6 is just the function of a line (can be written as y = x - 6) and it goes on forever in both directions, and for the other one with the square root, just realise that the square root accepts any value for x EXCEPT what makes it negative
like, for y=sqrt(x) the domain is [0, infinity) and the range is [0, infinity) too
the function only accepts positive or zero x values and outputs positive or zero y values
those are ur hints 😵💫
but anyways we can continue this later, u can just type .close for now until then if u wanna
karmic apex
Guys i have some homework that i need to be done in 2 hours. it is junior/senior level and i will pay the onw who makes it and able to explain it good 15 bucks. Anyone up?
gray isle
against server rules
gray isle
what is it then
gray isle
no monetary discussions here, people are volunteers
its also sus when people are willing to do that especially when there's a time limit
karmic apex
i will translate
karmic apex
no monetary discussions here, people are volunteers
its also sus when people are...
ok i wont pay but make a donation : )
gray isle
that's effectively the same as paying
karmic apex
no
it is not paying you are volunteers and i accept that but as a token of thank you i will make a donation unless you want to help me out without the donation
lone heartBOT
@karmic apex Has your question been resolved?
stiff tree
Hi
How to prove that 2x + 1 = y is a bijection?
magic falcon
Make polynomial function p using these. Answer in factored form.
the degree is 5
one zero is 0 multiplicity 2
the remainder when p is divided by (x + 1) is −40
the graph is tangent to the x-axis at (1,0)
2x^2 − 5x + 3 is a factor of p.
magic falcon
so i was thinking
degree of 5, 0 multiplicity 2, tangent to 1,0
that means that x^2(x-1)^2 and some other factor
zenith latch
that works
magic falcon
so i solve for the other factor
zenith latch
gotta get the other two condtions though
magic falcon
using the given quadratic functions
i find the zeroes of the quadratic equation
one of them should either be 0 or 1 and the other should be the final factor
but i got it wrong
i think it has something to do with when divided by x-1, = -40
magic falcon
that works
how though
zenith latch
how though
call the other one (x-r)
magic falcon
the zeroes of the given quadratic function is 3/2 and 1
zenith latch
and then i suppose you could just solve for r
magic falcon
hmm so i dont do anything with the quadratic function?
zenith latch
the zeroes of the given quadratic function is 3/2 and 1
does $x^2(x-1)^2(x-\frac{3}{2})$ work at all
@ocean seal smh
magic falcon
f(x) = x^2(x-1)^2(x-r)
f(-1) = -40
(-1)^2 (-2)^2 (-1-r) = -40?
4(-1-r)
-4 - 4r = -40
4r = 36
r = 9
zenith latch
oh do u have to scale it?
zenith latch
only need the factors
oh?
zenith latch
hmm maybe i should use the quadratic function
yeah i have no idea
let me try to graph
magic falcon
f(x) = x^2 (2x^2 - 5x + 3) (x-r)
f(-1) = -40
1 ( 2 + 5 + 3 ) ( -1 - r ) = -40
10(-1-r)=-40
-10 - 10r = -40
10r = 30
r = 3
damn why are the rs different
magic falcon
wait where did 2 come from
nvm i see
solve for a
the quadratic roots were right
thanks!
.close
fast tiger
lone heartBOT
fierce prairie
f(1) is asking for the graph's y position at x=1
fierce prairie
well f(1) is not a coordinate, just the y value
so just put 8
same idea for f(-1)
fast tiger
Didnt mean to close this lol
lone heartBOT
Didnt mean to close this lol
fast tiger
log36=2log6=2log2+2log3=2x+2y
What about the fractions ones? they seem a little more tricky
fast tiger
Wait, turns out x-4y is wrong @low quartz
fast tiger
Okay thanks
This is the next one I need help with
late mango
Okay thanks
This is the next one I need help with
multiply by the conjugate of 4-3i
fast tiger
Multiply 4+3i to the top and bottom?
late mango
yes
fast tiger
41/25 - 13i/25?
low quartz
srry
outer lark
its correct
fast tiger
Is that standard form tho?