It's not a "more accurate" answer, it's the right answer as opposed to the wrong one
#help-27
pine bay
so u js told me to do it but it was wrong
toxic grove
It has nothing at all to do with part b
toxic grove
Well yeah, it's how to check your answer to part a
ON your exam
It's how you prevent silly mistakes
pine bay
ikik
would that not just equal 2.4
just by looking at it
ur multiplying everything by 0 exept for 2.4
toxic grove
Exactly
pine bay
alr perfect
and as for the max height the baloon reaches
i can take my too zeroes, add them and divide by
2
to get axis of symetry
then plug that into my equation?
toxic grove
Yep, that's one way of doing it
pine bay
shorter way?
toxic grove
Because quadratics are symmetric equations
It won't work in general but it works for quadratics
General way involves calculus
pine bay
nah bro its only avaialbe in gr12
toxic grove
It's nothing to do with how simple they are, it's just a special case for quadratics
It doesn't matter because you're dealing with quadratics
pine bay
i need advanced functions, calculus, chemistry, physics and english to become an architectural engineer
pine bay
and im trying to get into waterloo with a 5-15% aceptance rate
pine bay
Well if you want the calculus way I can tell you that
no bro
ill get it marked wrong
its fine
maybe next year when im doing calculus
oh wait
yo
@toxic grove
can i not just complete the square to get it into vertex form then take the c vaalue and thats my maximum
toxic grove
That's another way of doing it
pine bay
im mad creative
on sum real shit
do u have the answer
im about to say it and i want u to tell me if its right
toxic grove
Yes I've had it written down for nearly an hour now
toxic grove
No
toxic grove
Yes
pine bay
plug it in
toxic grove
So what's h(2.7)?
pine bay
62.07
toxic grove
No
toxic grove
You did the same thing as last time
Exactl ythe same thing
You forgot the square
It's vitally ipmortant
toxic grove
Much better
pine bay
alright bro
its bed time ngl i got an exam 9am tmr
gota say bro w out u ion think id know shit for these last couple units
toxic grove
Good luck then
pine bay
preciate u bare man i added u if u ever tryna tutor me for sum cash or smth id appreciate it
u rlly helped on sum real shit
3 straight hours
pine bay
word bro
toxic grove
preciate u bare man i added u if u ever tryna tutor me for sum cash or smth id a...
Also thx
toxic grove
Godspeed
devout snowBOT
@pine bay Has your question been resolved?
kindred yacht
how to solve ii
devout snowBOT
how to solve ii
kindred yacht
i have factorized it already
graceful stone
i have factorized it already
x^3-y^3?
kindred yacht
strange arch
I used the identity
multiply numerator and denominator with (sqrt(7)+sqrt(5))
kindred yacht
multiply numerator and denominator with (sqrt(7)+sqrt(5))
why
graceful stone
For that crazy fraction, let x=7^1/2 and y=5^1/2
strange arch
because the denominator is (sqrt7 - sqrt5)
or to put it differently, say the denominator is a-b
if you multiply num and denom with a+b
you get in the denominator:
(a-b)*(a+b) = a²-b²
and since in our case a=sqrt(7) and b=sqrt(5)
you can easily just do a²=7 and b²=5
graceful stone
For that crazy fraction, let x=7^1/2 and y=5^1/2
Then you can simplify using that formula like how the problem want you to do
kindred yacht
you can easily just do a²=7 and b²=5
oh ok lemme try
kindred yacht
because the denominator is (sqrt7 - sqrt5)
what about the power dont we need to consider that
slender mirage
I think op already did the factorization and cancellation?
kindred yacht
I think op already did the factorization and cancellation?
yes i did factorize it
strange arch
oh did I miss it
kindred yacht
oh did I miss it
lol
graceful stone
I think op already did the factorization and cancellation?
Yes, but @strange arch is suggesting rationalizing the denom for some reason
slender mirage
how to solve ii
If you're done factorizing and cancelling, you're only left to evaluate (√7)² + (√7)(√5) + (√5)² are you not?
that's just 12 + √35 ?
kindred yacht
If you're done factorizing and cancelling, you're only left to evaluate `(√7)² +...
oh so i just sub the values like @graceful stone told
strange arch
because this doesn't look like the factorized version
strange arch
Yes, but <@1000186270078750740> is suggesting rationalizing the denom for some r...
result needs to have form c+dsqrt(35)
kindred yacht
my school suggested this solution but idk
slender mirage
that's the same thing
strange arch
ah right top contains the factor @graceful stone makes sense
slender mirage
my school suggested this solution but idk
You factorized, you cancelled the (x - y), and proceed to evaluate (x² + xy + y²)
is it not the same thing?
graceful stone
is it not the same thing?
Pretty much
The problem was dropping hints about factoring so i was trying to suggest that
But rationalizing the denom should give the same answer
kindred yacht
wait so can 1 person type out the easiest method and explain it
cuz im confused with so much stuff here
slender mirage
$\frac{x^3 - y^3}{x-y} = x^2 + xy + y^2 = (\sqrt{7})^2 + (\sqrt{7})(\sqrt{5}) + (\sqrt{5})^2 = 12 + \sqrt{35}$
woven radishBOT
kindred yacht
ok ig also the question says $\frac{x^3/2 - y^3/2}{x^1/2-y^1/2}
graceful stone
So @slender mirage is taking $x=7^{1/2}$ and $y=5^{1/2}$
woven radishBOT
Cris
slender mirage
||why ping 
||
graceful stone
To give credit sry
kindred yacht
So <@706934233012371577> is taking $x=7^{1/2}$ and $y=5^{1/2}$
then it should be 0.5 right?
kindred yacht
So 7^3/2 would be x^3
huhhhh
im actually so confused could you please explain it simpler
kindred yacht
If x=7^1/2, then x^3=7^3/2
yes
graceful stone
Similar if y=5^1/2 then y^3=5^3/2
kindred yacht
yes
graceful stone
how to solve ii
So you can rewrite the original fraction as $\frac{x^3-y^3}{x-y}$
woven radishBOT
Cris
graceful stone
And follow this solution
graceful stone
Np
strange arch
i get it now
should we leave the help channel open just in case? :]
toxic spire
So say we have 5 points on one side, 7 points on another and 6 points on another
toxic spire
The amount of triangles we can make is 5x6x7 right
How is that different from adding 5+6+7=18 and taking the combination of that
Aka 18x17x16/6
816
lilac mango
The amount of triangles we can make is 5x6x7 right
no
toxic spire
?
toxic spire
Yes
lilac mango
so to explain why the calc isnt 5x6x7
toxic spire
Sorry about the delay discord mobile app for some reason is shitting itself
toxic spire
Yes
lilac mango
right
so while theres probs a few ways to do it
i'd do it using casework
so split it into calculations for each case then add them up all together
- each point is on a seperate side
toxic spire
so split it into calculations for each case then add them up all together
So take one point on the 5th side
As a case
lilac mango
- one point is on a side while the other 2 points is on a second side
toxic spire
And use the other two sides as two points??
toxic spire
- each point is on a seperate side
Ohhh
Ah i get ot
Btw i gotta ask
Do you have any book recommendations/class recs for permutation and combination and stuff
toxic spire
- each point is on a seperate side
This case would be 5x6x7 right?
lilac mango
This case would be 5x6x7 right?
yeah
toxic spire
Wait would there be double counting
lilac mango
wdym
toxic spire
Ok nah we're good
toxic spire
wdym
Like if a,b,c is a triangle, b,a,c is same triangle
So we'd have to divide by the number of those repeated counts
Doesnt seem like thats a prob here tho
lilac mango
na should be all good
toxic spire
Ye
lilac mango
then for the next case
toxic spire
- one point is on a side while the other 2 points is on a second side
In this case we have to split it in to two more cases I think
lilac mango
if we pick the side with 5 points first
toxic spire
Take 1 point on 5 side as starting
lilac mango
yep
toxic spire
Take the point with 7 side
lilac mango
then you can pick any of the remaining 13 poinst
toxic spire
Pick another point
toxic spire
I was gonna do it like
Pick a another side
In this case 7
Pick a point on there
6 points remaining
So 5x7x6 for that side
Then pick the 6 point side
Take one point, 5 points remaining
5x6x5
Add those two cases together?
toxic spire
then you can pick any of the remaining 13 poinst
This would include both the 7point and 6 points and we'd end up with the prev case coming me thinks
lilac mango
wait
im gonna label it
for case 2, one from one side and the other 2 from another
toxic spire
Ye
lilac mango
2 from AB) 5C2 * 13
thats what i was trying to get to sorry
you pick one side
and then you pick the 2 from that side
to prevent the double counting
2 from BC) 6C2 * 12
2 from AC) 7C2 * 11
toxic spire
Im ngl i havent studied combinations yet 💀
lilac mango
the C just represents choose
toxic spire
Sorry
toxic spire
So 5x7x6 for that side
Will this case have double counting?
Doesnt seem like it
Wait cant we just group the 6 point and 7 point side together as 13 points
lilac mango
ya
toxic spire
Take one point from the 5 side
lilac mango
but thats the one that you'd pick one from
lilac mango
no because then you'll
double count
itll clash with choosing 1 point from each side
because from the 13 remaining points
theyre not all on the same side
if you wanted to group the rest
you'd have to only pick 1 from the 13
and pick 2 on the same side
toxic spire
Huh
lilac mango
2 from AB) 5C2 * 13
which is essentially this
lilac mango
cuz
toxic spire
Lemme think
lilac mango
say you pick a point from the side with 5 points right
as you said, you'll have 13 points remaining
toxic spire
Yes
lilac mango
our first case was that
toxic spire
On the other side yes
lilac mango
each point is on seperate sides
your suggesting to pick 2 points from the remaining 13 correct?
toxic spire
Yep
toxic spire
Regardless of seperate side
lilac mango
if you pick 2 that aren't on the same side
then you end up picking 1 from each side
which clashes with your first case
toxic spire
which clashes with your first case
No im uh saying cant we do the whole thing via that one operation without splitting it into cases
lilac mango
there is another way to do it, which is to find the total combinations then subtract the cases where the points chosen are all on the same line
lilac mango
No im uh saying cant we do the whole thing via that one operation without splitt...
oh without the first case
restive river
It doesn't it would to be too large
toxic spire
From what i think the 5x13x12 should double count prob
restive river
You have to find the multiplier for each angle
toxic spire
So we need to divide it by 6
lilac mango
yeah 5 x 13 x 12 is 780
restive river
Yes
lilac mango
too high
restive river
But u need the multiplier
toxic spire
Sine if we have 3 points a,b,c they can be arranged in 6 ways
So there would be 6 times repeated count
restive river
No
toxic spire
So just divide by 6?
restive river
Its not
lilac mango
i'm getting 751 i think 780/6 is too low
toxic spire
Damn
lilac mango
Its more then 900
no
lilac mango
i think if you do it that way
toxic spire
Wait wait
lilac mango
youll have to also make an operation where you do 6
toxic spire
I dont think we need to divide by six
lilac mango
and one from 7
toxic spire
We are only selecting 1 point from 5 in the first place
So 5 wouldnt factor into the repeated count
So itd be 780/2 maybe?
toxic spire
youll have to also make an operation where you do 6
Oh right
lilac mango
because your assuming you start with the 5
toxic spire
That 5 thing just takes from the 5 side
lilac mango
when you can also start with the 6 and the 7
toxic spire
And doesnt consider just 6 and 7
lilac mango
yep
restive river
The angle doesn't contain just 6 and 7
toxic spire
What
toxic spire
How?
restive river
Or where it repeats
toxic spire
Uh
restive river
Can u show where it repeats?
toxic spire
What the fuck do angles have to do with this
toxic spire
....
restive river
Where is the question?
toxic spire
Huh?
restive river
Find the matrices
toxic spire
So say we have 5 points on one side, 7 points on another and 6 points on another
This
Is this guy trolling or what
lilac mango
Argh my brain is frying
if you study combinations this question becomes much easier
i cant think of a way to do it without it
toxic spire
Oh
lilac mango
its definitely possible i just can't work it out
toxic spire
Well im trying to do this question
I just made that other question up to get a base
That question doesnt use combinations
restive river
717?
toxic spire
Its 717 yes
toxic spire
Howd you get it
restive river
Consider a rectangle ABCD having 5,7,6,9 points in the interior of the line segments AB, CD, BC, DA respectively. Let a be the number of triangles having these points from different sides as vertices and B be the number of quadrilaterals having these points from different sides as verticies then (B -a) is equal to:
-
795
-
1173
-
1890
-
717
It is 4, 717
toxic spire
What
lilac mango
Howd you get it
you can calculate alpha
toxic spire
Ok bruh
lilac mango
by
so you have the sides AB BC CD and DA yes
all the possible combinations is just
AB * BC * CD
AB * CD * DA
AB * BC * DA
CD * BC * DA
wait
i think that's right
so
ab has 5, bc has 7, cd has 6 and da has 9 points
so
restive river
yes
toxic spire
Ok uh mind if i ask one more question
restive river
Yes
toxic spire
Got it
lilac mango
beta is just AB * BC * CD* DA = 1890
restive river
Correct
lilac mango
then subtract ya
toxic spire
I assume for the rectangle we just do the other
restive river
Yes
lilac mango
yep
toxic spire
Okay thanks
restive river
Correct
restive river
Yes go ahead
lilac mango
i can try ya
restive river
90
toxic spire
Idk where to start on that one
restive river
Is it 90?
lilac mango
hang on
u need to choose f(1) and f(2)
so if the set is {1, 2, 3, 4, 5, 6}
6 choicse for f(1) and 6 choices for f(2)
not sure if i'm going the right way with this
restive river
The total numbers of functions f : {1,2,3,4} > {1,2,3,4,5,6} such that f(1) + f(2) = f(3), is equal to
-
60
-
90
-
108
-
126
ERM, 90
toxic spire
6 choicse for f(1) and 6 choices for f(2)
How do you get 6 choices
Oh is it because of the range?
lilac mango
the codomain is 1,2,3,4,5,6
restive river
The total numbers of functions f : {1,2,3,4} > {1,2,3,4,5,6} such that f(1) + f(...
If this is the question
lilac mango
so the possible outputs is 6
toxic spire
Got it so
lilac mango
so the total combinations is 36 for f(1) and f(2)
toxic spire
so the possible outputs is 6
f(3) has 6 values it can take
lilac mango
yep
toxic spire
Wait no
5
F(3) cant take the value 1
Cause theres no zero in domain
The minimum is 2
1+1
lilac mango
i was more thinking to count the solns such that f(1) + f(2) is smaller or equal to 6
toxic spire
i was more thinking to count the solns such that f(1) + f(2) is smaller or equal...
Yeah but see
f(3) can take values 2,4,5,6
So if f(3)=2 then that means f(1)=f(2)=1
restive river
are u a learner like me
toxic spire
Hmmm
lilac mango
f(3) can take values 2,4,5,6
yes that's correct
restive river
Yes
toxic spire
My bad
toxic spire
that f(1) + f(2) = 2
Wouldnt that just be one comb
lilac mango
yep
which is theyre both 1
for f(1) + f(2) = 3, you have 2 combinations
which is (1,2) and (2,1)
restive river
Hm no
toxic spire
which is theyre both 1
Uh dude
The solution says theyre 6cases
Which is where im stumped
f(3)=2,(f(1),f(2))→(1,1)→6 cases
restive river
Yes
toxic spire
Thats what the solution says
restive river
Its right
toxic spire
Not sure where tf that came from
toxic spire
which is (1,2) and (2,1)
Any idea?
restive river
I can help you learn but you need to take the structure
lilac mango
Any idea?
no im not too sure with that sorry, if @restive river understands then they can help out
toxic spire
no im not too sure with that sorry, if <@456226577798135808> understands then th...
That dude is just trolling lol
But i think we kinda screwed up
restive river
I'm not
toxic spire
Because uh
f(1) should also have the codomain value from 1 to 6
Same with f(2)
Its only f(3) that doesnt have the value 1
toxic spire
no im not too sure with that sorry, if <@456226577798135808> understands then th...
Oh shit dude
I think i got it
So we have a singular case for f(3) right
f(1)=f(2)=1
lilac mango
mhm
toxic spire
mhm
Im thinking that f(1) can have 4 values that give 1
Since the domain is 1,2,3,4
Wait no its already specified which number we take thats 1
Okay bruh
@lilac mango should i close this or leave it open for help
lilac mango
<@720162596484939817> should i close this or leave it open for help
not rlly sure where to go with this, leave it open for help and if you still cant get it ping helpers role
toxic spire
Aight got it
Tysm for your help so far
Uh thanks for your help?
The question is above
....
How the fuck they got 90
Whats the point of knowing the answer if you dont know how they got it
devout snowBOT
@toxic spire Has your question been resolved?
devout snowBOT
@toxic spire Has your question been resolved?
toxic spire
So uh any new help
devout snowBOT
@toxic spire Has your question been resolved?
devout snowBOT
@toxic spire Has your question been resolved?
restive river
just check for f(1) = 1
then f(1) = 2
and so on
posting again so dont have to scroll
and f(4) has no constraints on it so it can be any of the 6 values in the co-domain
rough idea
so that f(3) = f(1) + f(2) doesn't go beyond 6
restive river
@toxic spire
toxic spire
and f(4) has no constraints on it so it can be any of the 6 values in the co-dom...
Yes i got that
But how does that help with the question
Because the question has the relation f(1)+f(2)=f(3)
f(4) isnt a part of that
restive river
rough idea
check this
restive river
f(4) isnt a part of that
you still need to map 4 to something in the co-domain
you have 6 options
so 15 * 6
toxic spire
rough idea
Yeah i got that
toxic spire
you still need to map 4 to something in the co-domain
Ugh
It still isnt clicking
Why are we using that as the conditions for it
toxic spire
Yes
restive river
and you still have to map 4
toxic spire
Yep
toxic spire
Why are we multiplying it by the values of f(1) tho
toxic spire
Sorry not the values
The amount of options f(1) has
What does that have to do with f(4)
Wait
restive river
write down all possible funcs for f(1) = 5
toxic spire
Since it has to satisfy the f(1)+f(2=f(3) thing
restive river
its not much
restive river
no
toxic spire
Wut
restive river
write down all possible funcs for f(1) = 5
do this, you'll see
f(1) = 5 then f(2) can only be 1
right?
toxic spire
Yes
restive river
so f(3) is 6
toxic spire
Yes because every domain element needs a codomain ye
toxic spire
you've 6 options
1,2,3,4,5,6 ye
restive river
so what's the doubt?
toxic spire
Why are we multiplying six by the numbers of options of f(1)?
Here f(3) can be 2,3,4,5,6
f(3)=2,(f(1),f(2))→(1,1)→6 cases
f(3)=3,(f(1),f(2))→(1,2),(2,1)
→2×6=12 cases
Here
We are multiplying the 2 cases of f(3)=3 which is (1,2) (2,1) by 6
To get 12
Why do we need to do that dont we already have which cases satisfy the relation
restive river
Why do we need to do that dont we already have which cases satisfy the relation
f(4) can be any of 1 to 6 though
1,2,3,(1 to 6)
and
2,1,3,(1 to 6)
toxic spire
Yes so f(4) has 6 options i get that, but what does that have to do with us finding which cases satisfy f(1)+f(2)=f(3)
restive river
Yes so f(4) has 6 options i get that, but what does that have to do with us find...
it doesn't have anything to do when finding the cases
but you still haveto consider f4 when finding how many fns there are
toxic spire
Then why are we multiplying the number of cases we get by 6
restive river
1,2,3,(1 to 6)
and
2,1,3,(1 to 6)
.
toxic spire
1,2,3,(1 to 6)
and
2,1,3,(1 to 6)
Cant a function only have 1 value
restive river
does this help? 😅
toxic spire
does this help? 😅
Wait so is it like when the relation f(1)+f(2)=f(3) is satisfied f(4) can take any of the 6 values?
Oooh
AH
I think i get it
So if like
We take it in a bracket(just for clarity) as {f(1),f(2),f(3),f(4)}
In the case of f(3)=2, then f(1) and f(2) will both be 1
And f(3) is 2
restive river
Wait so is it like when the relation f(1)+f(2)=f(3) is satisfied f(4) can take a...
yeah
restive river
yess
toxic spire
Thank you so much man
restive river
no prob
restive river
haha, happens
toxic spire
Got it
restive river
^
devout snowBOT
devout snowBOT
Available help channel!
tender cedar
Hello, I'm confused how adding "b" to both sides equals 5/3b can anybody provide insight?
devout snowBOT
Hello, I'm confused how adding "b" to both sides equals 5/3b can anybody provide...
mystic scarab
$$\frac{2}{3} + 1 = \frac{2}{3} + \frac{3}{3} = \frac{2 + 3}{3} = \frac{5}{3}$$
woven radishBOT
Alberto Z.
mystic scarab
If this is not clear, then I strongly suggest you back up a little bit and revise basic algebra
Because it's fundamental for understanding equations with letters appearing besides numbers
tender cedar
got it thank you! writing it out makes it clear
wide elm
devout snowBOT
wide elm
sketch
I need final speed on contact and time of position being 0
I wrote the function as
f(y) = 39 + 21t - 0.5gt^2
where g is the magnitude of acceleration due to gravity, 9.80 m/s^2
ok I got it
I messed up with my function in my calculator
slender mirage
wide elm
and the program didn't want the velocity as negative
(I put 32 instead of 39 somehow)
But it didn't specify that it was the magnitude only :(
Thank you for coming to help :)
.close
arctic mist
Trying to figure out where/how I need to start to get #17 done (finding the value of a,b,c,d)
Ignore #16
devout snowBOT
Trying to figure out where/how I need to start to get #17 done (finding the valu...
@arctic mist Has your question been resolved?
arctic mist
<@&286206848099549185>
slender mirage
Trying to figure out where/how I need to start to get #17 done (finding the valu...
start with a: 3/6 = 9/(9 + a)
then angle bisector theorem: 5/7.5 = (6 + 6 + c)/(9 + a + 4.5) gives c
then d/5 = 6/(6 + 6 + c) gives d
and lastly, I hope you can find b
devout snowBOT
devout snowBOT
Available help channel!
nimble sable
why are they using synthetic division if you can factor it normally
acoustic leaf
you can't perform partial fraction decomposition unless the degree of the denominator is higher than the degree of the numerator
so, you have to perform the polynomial division to fix that first
nimble sable
you can't perform partial fraction decomposition unless the degree of the denomi...
or equal?
acoustic leaf
no, it has to be strictly higher
smoky nimbus
is + 2x not included right here?
Well you're doing partial fractions, that term isn't part of the fraction anymore
acoustic leaf
the 2x is pressent on both sides of the equation, so you can ignore it for the purposes of solving for A and B
devout snowBOT
devout snowBOT
Available help channel!
blissful gorge
i have no idea how to do this on a calculator
devout snowBOT
i have no idea how to do this on a calculator
gleaming socket
,rotate
woven radishBOT
blissful gorge
thanks
gleaming socket
First is to rearrange the equation in terms of x
blissful gorge
okay how
i apologize my skills with the calculator are equivalent to an average grandma on a nintendo switch
gleaming socket
Basically x = arccos (2/5)
blissful gorge
got it
gleaming socket
Now in your calculator you may have arccos or cos^(-1)
blissful gorge
it does yes
gleaming socket
What did you get?
blissful gorge
66.4218
gleaming socket
,calc (2/5)
woven radishBOT
Result:
0.4
,calc arccos (2/5)
woven radishBOT
The following error occured while calculating:
Error: Undefined function arccos
gleaming socket
Maybe it's set in degrees ?
gleaming socket
Instead of radians?
blissful gorge
i’m sorry i have to go
primal axle
Maybe it's set in degrees ?
yes
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daring barn
Hi, could anyone enlight me what characters should I use if I wanna denote coefficients or weights in an expression? Thanks
devout snowBOT
Hi, could anyone enlight me what characters should I use if I wanna denote coeff...
spare zealot
This may depend entirely on the context of the problem and conventions persuant to the topic
But in general, variables can be represented with whatever you'd like as long as you communicate what they represent
The standard form linear equation is generally Ax+By=C, but A, B, and C are only chosen because they're the first three letters in the English alphabet and generally easy to remember
The equation itself could just as easily be represented by Wx+θy=ξ and mean the same thing, as long as someone working with it understands what W, theta, and epsilon mean
daring barn
But in general, variables can be represented with whatever you'd like as long as...
If not using characters at the head of the alphabetic order, could you suggest some characters that are used the most?
spare zealot
Any particular subject?
daring barn
Bcoz I saw ppl using x, y in italy style.
Oh yes the subject
I'm doing a financial cost expression
spare zealot
Algebra tends to use x, y, and z for coordinates/experimental variables and i, k, m, and n for some formulas
Probability and stats use n, p, q, and some others
daring barn
by adding weighted components, I need some characters to denote the weights
daring barn
Algebra tends to use x, y, and z for coordinates/experimental variables and i, k...
should they be in italic style?
spare zealot
They don't need to be
It helps if x is if it's a more rudimentary field of math because younger students may confuse "x" for a multiplication symbol
But letters in formulas are generally understood to be variables
Subscript is used a lot to denote distinct variables of the same type
For example, the slope formula is $m = \frac{y_2 - y_1}{x_2 - x_1}$, where $x_1$ and $x_2$ are both x-component coordinates, but are different from each other (same for y)
woven radishBOT
al-jebruh
daring barn
Ah the subscript is so good. Also, if i'm hoping to do this financial expression in a linear regression style, which means the weights would be used as coefficients, is there suggestions abt which characters to use instead?
Nevermind, I think I just need to follow your explanation above 🙂
spare zealot
Weights afaik are usually just multuplied to variables
daring barn
Weights afaik are usually just multuplied to variables
you are right.
daring barn
Weights afaik are usually just multuplied to variables
Thanks for the help, I think I'm much clearer abt the character usages.
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severe nacelle
Here is my attempted solution for the question: Suppose f and g are boh functions that are uniformly continuous on the set A and both f and g are bounded on A. Show that the product of the 2 functions fg is also uniformly continuous on A. Is my attempt correct?
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Here is my attempted solution for the question: Suppose f and g are boh function...
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lofty drum
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winter patrol
!status
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What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above
viscid onyx
Apply trigonometry.
So for ∆RQM, you get
RQ/MQ = cos(60°)
Or RQ = MQ/2
So, RQ is half of MQ.
Now, look at ∆PQM, you get the angle(MQP) as 15° because angle(PQR) is 75° and angle(MQR) is 60°.
Now let's look at ∆PQR, it's a right angled triangle, so angle(RPQ) should be 15 degree.
So from this we get that PM = MQ = 18.
And hence, RQ = 9
lofty drum
Apply trigonometry.
So for ∆RQM, you get
RQ/MQ = cos(60°)
Or RQ = MQ/2
So, RQ is...
thank you but we did not learn any of that yet
we only learned basic geometry
.close
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lavish zealot
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remote charm
What's wrong here
copper shadow
What's wrong here
it is not clear ma dude
remote charm
it is not clear ma dude
It split the integral
And I'm supposed to get alpha as 30 and beta like -25
Here i got 10 and -12
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slender mirage
$\int_{n-1}^n \frac{{x} + 2[x]}{e^{{x}}} = \int_{n-1}^n \frac{{x}}{e^{{x}}} + \int_{n-1}^n \frac{2(n-1)}{e^{{x}}}$
woven radishBOT
slender mirage
Left side is just (e - 2)/e, Right side is 2(n - 1)(e - 1)/e
slender mirage
Yes I saw
remote charm
Bruh silly mistake
slender mirage
Add them and you should get: 5(e - 2)/e + 20(e - 1)/e
remote charm
I took x for [x]
remote charm
Add them and you should get: `5(e - 2)/e + 20(e - 1)/e`
Ye
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remote charm
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shut tendon
In our math book it is claimed that: "If the function 𝑓 has 3 roots, the inequality ax^3+4x^2+x>0 cannot have a solution for x>0 because in that case, the values of the function 𝑓 are necessarily positive in two intervals."
How can one intuitively determine the number of positive and negative intervals in a polynomial function of degree n? I kinda figured out it was true after considering the roots of the derivative. I realized that the roots of the first derivative aren't enough for the "direction changes" required for the function to only have a single positive interval. The textbook, on the other hand, doesn't offer a reasoning process. it just states this as a fact.
So my question remains: How can one intuitively determine the number of positive and negative intervals in a polynomial function of degree n?
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shut tendon
<@&286206848099549185>
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lost laurel
$(P \land Q) \lor (P \land \neg Q)$
devout snowBOT
$(P \land Q) \lor (P \land \neg Q)$
woven radishBOT
What a wonderful world!
feral agate
this is just P
yes
lost laurel
Thanks
north mountain
**What a wonderful world!**
P
lost laurel
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distant wave
The annual salaries of six employees of a company are as follows
$22,000, $35000, $22,000, $46,000, $57,000, $90000
get the standard dev
is my calculation correct im doubting my calculator
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woven radishBOT
Result:
272
small jackal
,calc 272/6
woven radishBOT
Result:
45.333333333333
sleek latch
560
236
236
340
590
248
248
360
620
260
260
380
655
275
275
400
690
290
290
420
725
305
305
440
760
320
320
460
795
335
335
480
835
352
352
510
875
369
369
540
915
386
386
570
955
403
403
600
995
420
420
630
1040
439
439
670
devout snowBOT
560
236
236
340
590
248
248
360
620
260
260
380
655
275
275
400
690
290
290
420
...
sleek latch
what is the pattern scheme for these numbers
steady robin
what is the pattern scheme for these numbers
what kind of pattern do you desire
i cant find anything in oeis but you could definitely do a polynomial interpolation
ancient sluice
Look at it in sets of 4
sleek latch
i cant find anything in oeis but you could definitely do a polynomial interpolat...
i think that
ancient sluice
There's a resemblance that continues till 4 sets of 4
sleek latch
it just says pattern scheme to me too
ancient sluice
Then the middle number starts incrementing by 15 instead of 12 and again after a few sets it increases by 7 !
sleek latch
hm let me s
sleek latch
Then the middle number starts incrementing by 15 instead of 12 and again after ...
wdym by incrementing?
sleek latch
i cant find anything in oeis but you could definitely do a polynomial interpolat...
have u tried yet
steady robin
have u tried yet
polynomial interpolation? hell nah i aint interpolating like 70 numbers
sleek latch
polynomial interpolation? hell nah i aint interpolating like 70 numbers
what do y think the pattern is by looking at the first few terms
steady robin
i agree with what xor said that you can group it into 4 and then theres a pattern
sleek latch
i agree with what xor said that you can group it into 4 and then theres a patter...
ty
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finite briar
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finite briar
Y'all could someone check my integration?
finite briar
err ignore the last step on the second page, should pi/2 instead of pi
<@&286206848099549185>
anyone???
neonnnn!
rugged sparrow
jee 25?
finite briar
i am the kraken guy..
@rugged sparrow
<@&286206848099549185>
<@&286206848099549185>
Okay so I messed up somewhere
Because my integrals finally diverged xd
slender mirage
Just a sec. What is it that I should be seeing?
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finite briar
+ what is the problem¡?
check 2nd page its in reverse order
slender mirage
Holy.. what are these
finite briar
Okay wait am stupid..why am I evaluating Jk at 0
finite briar
Holy.. what are these <:blobcry:971797574916907028>
Mse integral xd
I:ll send link to u on dm if u want tmrw
I don't have it on phone
slender mirage
cannot , the order is not very well organized and readable :c at least for me
perhaps someone knowledgable might be able to differentiate between the steps better
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valid tusk
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valid tusk
I'd like to check my work
winter torrent
valid tusk
ty!
working on another one like that rn)
i got this for the first two but im not sure if thats correct?
it's one of those im not sure which one
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hasty flame
True or false? If the slope of the line is -3, then the line goes down 1 and right 3
devout snowBOT
True or false? If the slope of the line is -3, then the line goes down 1 and rig...
hasty flame
I thought i had a grasp on simple algebra but apparently not
what does the "the line goes down 1 and right 3" mean??
wind mason
True or false? If the slope of the line is -3, then the line goes down 1 and rig...
quite the opposite.
If the slope of a line is -3, then the line goes down 3 and right 1.
what you have just described is a line of slope -1/3.
wind mason
what does "the line goes down" mean?
a kind of "interval of steps".
here, let me show you.
wind mason
recall that $\text{slope}=\frac{y_2-y_1}{x_2-x_1}$, where $(x_1,y_1)$ and $(x_2,y_2)$ are points on the line.
woven radishBOT
;(
hasty flame
for some reason I was thinking it had something to do with transformation which made zero sense
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sick leaf
Slightly confused on what is happening here>
Why do we have a (-1/x) and why do in the second step there is an extra negative
thin fern
Slightly confused on what is happening here>
Why do we have a (-1/x) and why do...
The -1/x is just from differentiating ln
sick leaf
The -1/x is just from differentiating ln
But why is that -1/x instead of positive?
I think it's going the chain rule so
dy/du is -1/x
du/dx is d/dx (-x)
But then is the u just -x?
thin fern
The derivative of ln(x) is 1/x as you probably know. It just takes the reciprocal of whatever function is inside
so d/dx(ln(-x)) = 1/(-x)
sick leaf
so d/dx(ln(-x)) = 1/(-x)
Yeah but why would 1/(-x) = 1/x in this case?
Ok nvm it's the second step
thin fern
Right remember you need to apply the chain rule
and the derivative of -x is -1
so there's an extra negative
sick leaf
Ok yeah I got the hang of it
Remind me again though, is the u just -1?
So g(u) where u=f(x)
In(u) where u = -x ?
thin fern
Yes
sick leaf
So dy/du becomes 1/(-x) and du/dx becomes -1
OH ok
Yeah great make sense now
Thanks
thin fern
sick leaf
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dry oak
hi, how does radiation work? is it like invisible fire or smthing?
wicked turtle
seems beyond the scope of a math server, have you tried the physics server? see #old-network
potent tusk
I dunno maybe it is
dry oak
seems beyond the scope of a math server, have you tried the physics server? see ...
ill ask there, thanks
regal moat
hi, how does radiation work? is it like invisible fire or smthing?
Its the emission and propagation of energy in the form of waves or particles
Usually by photon
Sometime other particles
But mainly photon
topaz axle
that's not what they meant
regal moat
that's not what they meant
huh?
topaz axle
people mean ionising radiation
regal moat
Sometime other particles
are this
quaint citrus
invisible fire is probably how they explained it back in the 1400s
topaz axle
you;re explaining "invisible light" but they could mean nuclear decay type of thing
but it's not clear which one maybe you guessed right
it's invisible fire, it happens to the atoms, so you can't stop it, but it gets more intense if you bring it in a pile
just from the amount of material close together
dry oak
ok i continued this in the physics server so i didnt check in on this channel
im watching chernobyl series from hbo
wicked turtle
invisible fire is probably how they explained it back in the 1400s
apparently electricity was referred to as the "subtle fire" well into the 1700s
dry oak
and i dont understand how radiation works, so i just want to learn out of curiousity
regal moat
and i dont understand how radiation works, so i just want to learn out of curiou...
Its just usually photon which high energy
Shoot the eletron of the atom
Which excitize it, and ionize it
Death basically (if ionize enough)
quaint citrus
apparently electricity was referred to as the "subtle fire" well into the 1700s
ah wow interesting
topaz axle
and i dont understand how radiation works, so i just want to learn out of curiou...
some atoms are unstable, they have a chance to blow up every moment, it's literally random
one example is potassium-40, the stuff in bananas
if you put alot of it close together it intensifies like i said
nuclear batteries work like that
it's just a tiny thing that's constantly hot, you use heat to make electricity, in space probes and rovers and stuff like that
apart from heat it shoots ionizing radiation, in 3 types
regal moat
Anyone has those old ceramic like plate and bowl with paint made from uranium compounds
dry oak
makes sense, yeah this is to my understanding basically how nuclear plants work as well, but im more curious about how it affects us and other things, like it can burn us, it can destroy our cells from within, it penetrates most things, it gets carried in the wind and clouds, it contaminates things like clothes and metals, how does all that work?
topaz axle
it's like microwave oven type of thing, but for some reason it gets absorbed by dna at low energy
like if you point a microwave at yourself you will die from burns before you get dna damage
but not with this thing
topaz axle
makes sense, yeah this is to my understanding basically how nuclear plants work ...
the thing that gets carried and contaminates is the dust, the actual chemicals
the radiation can't do that