#help-43
boreal girderBOT
native shard
,,
\begin{align*}
8x^2 - 12x + 10x - 15 &= (8x^2 - 12x) + (10x - 15)\
&= 4x(2x - 3) + 5(2x - 3) \
&= (4x + 5)(2x - 3)
\end{align*}
boreal girderBOT
knief
drowsy cedar
Where'd you get the 12x and 10x from
native shard
i told you before
i want two numbers that multiply to 8(-15) = -120 but add to -2
in general if you have ax^2 + bx + c then you look for two numbers whose product is ac and whose sum is b
then you rewrite bx as the sum of those two
and split off into pairs of two terms
factor each pair individually
native shard
**knief**
then take the greatest common factor out as i did in the last step here
would you like another example?
drowsy cedar
that seems way more confusing
drowsy cedar
it just seems like a whole lot of extra work
native shard
compared to splitting into a multitude of cases with guess work?
are you kidding?
it arrives at the answer without guessing and working through possible cases
the only "guessing" you're doing is figuring out how to rewrite bx
but thats fairly simple
drowsy cedar
Wait can you do 5x²-13x-6=0
maybe it'll make more sense then because I got that one right
native shard
sure. so we want two numbers that multiply to 5(-6) = -30 but add to -13. it shouldnt take long to realize -15 and 2 work
so we write
$5x^2 - 13x - 6 = 5x^2 - 15x + 2x - 6 = 5x(x - 3) + 2(x - 3) = (5x + 2)(x - 3)$
boreal girderBOT
knief
drowsy cedar
Is the 15x becoming the 5x(3 bit?
boreal girderBOT
knief
native shard
using my method
native shard
Is the 15x becoming the 5x(3 bit?
wdym
native shard
**knief**
in which step?
,,
\begin{align*}
5x^2 - 13x - 6 &= 5x^2 - 15x + 2x - 6\
&= (5x^2 - 15x) + (2x - 6)\
&= 5x(x - 3) + 2(x - 3)\
&= (5x + 2)(x - 3)
\end{align*}
boreal girderBOT
knief
native shard
What does the -15x turn into
it doesn't turn into anything, we just factor it with 5x^2
drowsy cedar
Ohhhhh I see
native shard
yes very good
it doesn't matter the order in which you write them btw
you can do 6x^2 - 3x + 4x - 2 or 6x^2 + 4x - 3x - 2
you'll get the same result
if you were wondering
drowsy cedar
6x²+4x-3x-2
drowsy cedar
Uhhhhh
native shard
take the greatest common factor
drowsy cedar
2
drowsy cedar
For 6 and 4?
drowsy cedar
I have no idea
native shard
2x(3x + 2)
drowsy cedar
^2 is ²?
native shard
yes
drowsy cedar
ahhh ok
native shard
the term involving x^2 always has a factor of x
the other one will just be a constant
but ok now for the important bit
we wrote 6x^2 + 4x = 2x(3x + 2)
our goal is to then factor out 3x + 2 from the other pair
so what do we need to factor from -3x - 2 to get this?
drowsy cedar
1?
native shard
-1
native shard
$6x^2 + 4x - 3x - 2 = 2x(3x + 2) + -1(3x + 2) = (2x - 1)(3x + 2)$
boreal girderBOT
knief
native shard
should we try another one
drowsy cedar
yea
boreal girderBOT
knief
native shard
you tell me what we do first
grim cairn
you tell me what we do first
Im ngl i forgot how to factor these im so addicted to using my calculator
native shard
Im ngl i forgot how to factor these im so addicted to using my calculator
you can read the last 20 minutes of conversation here
grim cairn
you can read the last 20 minutes of conversation here
🙏
drowsy cedar
So find numbers that times to -45 and add to -4x
grim cairn
I remember there were like 3 diff approaches
arctic portal
you tell me what we do first
quadratic eq bashing! /jkjk 
native shard
So find numbers that times to -45 and add to -4x
any luck?
drowsy cedar
-9 +5
native shard
make sure you include the + in the middle
3x(5x - 3) + 1(5x - 3)
but yes
and then?
drowsy cedar
So 3x+1 and 5x-3
native shard
yep
drowsy cedar
this makes sense
native shard
i told you
drowsy cedar
native shard
do you have any more on your homework
drowsy cedar
Yeah alot, I'm actually studying for a test
native shard
i'm sure this will help
drowsy cedar
are you irish too??
drowsy cedar
Ohhh xd
native shard
your pfp sticks out
drowsy cedar
Yeah I think so
native shard
you used to have an irish flag in your bio
drowsy cedar
Still struggling
native shard
i have a stupid memory lol
drowsy cedar
I have a test on Monday and i just feel so lost which is why I'm studying now
Hopefully it will get easier as I go on
drowsy cedar
Quadratic equations is only chapter 2.1 and I gotta do all the way up to 2.10 so it's gonna be fun
drowsy cedar
I feel like the chapters are just random stuff thrown together but I really need to lock in more
drowsy cedar
Technically yea lol but I think it's more like chapter 2 part 1 and chapter 2 part 10
grim cairn
The way id do it is find the product ac then find factors which sum to give b
Consider a random equation my own equation
$$2x^2+5x+2$$
Then find factors of $2\cdot 2$ which is $4$ and $1$ or $2$ and $2$
Since $4+1=5$ lets use that then we get $\frac{(2x+1)(2x+4)}{2} = (2x+1)(x+2)$
boreal girderBOT
(☞ ͡° ͜ʖ ͡°)☞ (Klein Mysteries)
native shard
ok but it isn't clear how you continued from "then we get"
which is what she was confused by
factoring by grouping makes this clear
grim cairn
The 2 comes from a
But then we'd need to divide by 2 because we want the coeff of x^2 to be 2
native shard
no this isn't a legitimate approach that works on all problems
grim cairn
no this isn't a legitimate approach that works on all problems
?
Give me an example where this doesn't work
native shard
you'd have to consider the potential factors of the leading coefficient and then do case work on deciding the order for the constants
do this
factoring by grouping removes this guessing
grim cairn
factoring by grouping removes this guessing
Ur not guessing tho?
native shard
how did you know it wasn't (2x + 1)(x + 4) without actually distributing
or sorry
- 4
grim cairn
how did you know it wasn't (2x + 1)(x + 4) without actually distributing
What
Cuz then coeff of x squared wluld be 4
We want it to be 2
native shard
- 4
native shard
hold on this is a bad example because i keep fucking up the constants lol
grim cairn
hold on this is a bad example because i keep fucking up the constants lol
😭😭😭😭
Theres only one factor which works it not guessing at all
And then we divide one parenthesis by the coeff of a
native shard
yes this is why its a shit example
grim cairn
Your grouping method is great for multivariable factoring
native shard
do the one i suggested
grim cairn
But in single variable factoring this method imo is preferred
grim cairn
do the one i suggested
I need paper one sec
native shard
your method literally only makes sense on trivial ones like this where there are no cases
grim cairn
your method literally only makes sense on trivial ones like this where there are...
Alr ima try it calc allowed right
grim cairn
this shouldn't be difficult
Factors of 120
native shard
i mean the numbers are - 15 and 2
go ahead
you then need to decide if your factors should be like (8x + ...)(x + ...) or (4x + ...)(2x + ...)
grim cairn
i mean the numbers are - 15 and 2
Ok bet
native shard
and you dont really have a way of doing this
in your example the leading coefficient and the constant term were prime
so there weren't any cases really
native shard
not so simple when they are composite
grim cairn
Ive done the question u gave
native shard
ok lets see the method
native shard
without just "oh i checked and this worked"
grim cairn
$8x^2-2x-15=0$
We shall use the factors $10$ and $-12$
We get:
$\frac{(8x+10)(8x-12)}{8} = \frac{(8x+10)(8x-12)}{2\cdot 4} = (4x+5)(2x-3)$
Cba to fix error
U see my working
grim cairn
😊
Anyways like i said
I prefer ur method for multivariable factoring
However for single variable i think this is veryyy simple
boreal girderBOT
(☞ ͡° ͜ʖ ͡°)☞ (Klein Mysteries)
grim cairn
I was taught three ways
native shard
i thought you were just guessing
😭
and correcting
but you can actually always just take the leading coefficient in each factor then divide by the leading coefficient and cancel whatever redundant constant factors you have
lemme prove this to myself
that it works in general
grim cairn
that it works in general
Alr
I also remember learning a thrid way which is just not something ud ever use
native shard
so lets assume $h, k$ are such that $h + k = b$ and $hk = ac$. then [\frac{(ax + h)(ax + k)}{a} = \frac{a^2x^2 + a(h + k)x + hk}{a} = \frac{a^2x^2 + abx + ac}{a} = ax^2 + bx + c]
nice
boreal girderBOT
knief
grim cairn
i apologize sir
Its fine lol
compact pewterBOT
Available help channel!
woeful dock
compact pewterBOT
woeful dock
ive solved this problem in another method, but i wanna know if it's possible to solve it this way, im stuck
vale star
Try to add the 1st two terms
And try to use the concept that sum of two roots is -b/a
And product is b/a
woeful dock
Try to add the 1st two terms
yes ,that is the method i used at first to solve the problem
i wanna know if there is a way to solve it using the method ive shown in the pictures
vale star
It's not exactly the same way
I can solve it and send u in a minute to clarify tho there is a no answer policy
According to question
Ratio of two roots is m:n
So u should substitute the m/n and n/m with the roots and add 1st 2 terms
And then js place the sum and product
They would end up being 0
If u dont get it ,i will send the alternative
Oh wait i got ur question
woeful dock
According to question
Ratio of two roots is m:n
So u should substitute the m/n ...
yeah im saying that ive solved it this way already.
vale star
At thee last line
It should be 1
2a/2a=1
woeful dock
oh right forgot to make that correction,
ive written it correctly after that line
woeful dock
this is what ive done so far
woeful dock
Lemme write it down
okay
vale star
vale star
this is what ive done so far
Lemme try from here
vale star
this is what ive done so far
These bring up complex numbers
Which is complex
woeful dock
yeah, this is convenient way of doing it, i was just curious if there are others ways of solving it
woeful dock
These bring up complex numbers
Which is complex
ya,lol
vale star
There prolly r other ways but better make it easier for u to complete timely in exam
woeful dock
i mean is there a way you could tell whether a problem is solvable in a specific method or not?
because it is especially annoying during exams when i am halfway through solving a problem and then i just get stuck, and then after a while i figure out it's way easier to solve in some other method
woeful dock
There prolly r other ways but better make it easier for u to complete timely in ...
yeah
vale star
i mean is there a way you could tell whether a problem is solvable in a specific...
Each type of math has different ways to go by it
U js need to figure it out
But for this one substituting is easier than going for the other approach
woeful dock
Each type of math has different ways to go by it
U js need to figure it out
But ...
i see
got it
thanks for the help
.close
compact pewterBOT
compact pewterBOT
Available help channel!
hasty star
I tried to apply the steps that i was taught : find the n-th derivative of f general form by using the first few derivatives to intuitively get to it and then prove it with math induction, but i can't seem to figure it out.
compact pewterBOT
I tried to apply the steps that i was taught : find the n-th derivative of f gen...
quartz yoke
I tried to apply the steps that i was taught : find the n-th derivative of f gen...
what's the term near e^y^2?
is that an 8?
quartz yoke
non o
quartz yoke
i believe you're reffering to y^6
times e^whaty^2
compact pewterBOT
@hasty star Has your question been resolved?
hasty star
<@&286206848099549185>
compact pewterBOT
Show your work, and if possible, explain where you are stuck.
@hasty star Has your question been resolved?
cyan slate
$f(y)=y^6e^{2y^2}$
boreal girderBOT
rays
cyan slate
I tried to apply the steps that i was taught : find the n-th derivative of f gen...
show your work
compact pewterBOT
@hasty star Has your question been resolved?
strange pendant
compact pewterBOT
boreal girderBOT
Renato
strange pendant
Hey, idk how to start
compact pewterBOT
@strange pendant Has your question been resolved?
strange pendant
How can I use little fermats
compact pewterBOT
@strange pendant Has your question been resolved?
twin salmon
I’ll give you some help. First check if 2 divides this sum or 3 divides the sum (since these are the prime factors of 6). Then without loss of generality suppose $p > 3$ so $\gcd(p,6) = 6p$. Now apply Fermat’s little theorem to each of the summands and sum the result. Then repeat for 6 (now without Fermats theorem of course). Let x be your expression. If $x \equiv a \mod p$ and $x \equiv b \mod 6$ then $a \equiv b \mod \gcd(6,p)$ so $a \equiv b \mod 6p$. This will simplify the problem by a lot I think
boreal girderBOT
Beth
strange pendant
I’ll give you some help. First check if 2 divides this sum or 3 divides the sum ...
The problem is that 3 does not divide 374
twin salmon
The problem is that 3 does not divide 374
Okay. Have you tried what I asked?
strange pendant
Okay. Have you tried what I asked?
I need more handholding
twin salmon
Have you checked if 2 or 3 is a solution?
strange pendant
Ok let's try p = 2
12 | 2x17^2 + 2x45^{4+2-1} -374 + 24
@twin salmon
I guess this is when I pull up a calculator?
twin salmon
I guess this is when I pull up a calculator?
If you want yes
twin salmon
Well. No you are doing modular arithmetic so you can calculate the remainder of 45 mod 12 instead
strange pendant
Yess
I like dat
2x17^2 + 2x45^{4+2-1} -374 + 24 = 0 (mod 12)
2x17^2 + 2x45^{4+2-1} = 350 (mod 12)
strange pendant
Ok
strange pendant
350 = 2 ( mod 12)
Wait
strange pendant
350 = 2 ( mod 12)
2x17^2 + 2x45^{4+2-1} = 2 (mod 12)
What is the problem with this?
@twin salmon
twin salmon
Well, nothing. You have then shown 2 is not a solution
strange pendant
How
twin salmon
How
Well 2 is the remainder after dividing by 6(2) =12
For division we would need a remainder of 0 (remember remainders are unique)
strange pendant
Care to elaborate
twin salmon
Care to elaborate
For any integers an and b where b is positive. There exists unique integers q and r (called the quotient and remainder respectively) such that $0\leq r < b$ and $a = bq + r$ ( this is the Euclidean algorithm). It follows $a \equiv r \mod b$. Conversely if $a \equiv r \mod b$ and $0 \leq r < b$ then $a = bq + r$ for some integer $q$, which by uniqueness in the Euclidean algorithm implies $r$ is the remainder after dividing $a$ by $b$
boreal girderBOT
Beth
twin salmon
2x17^2 + 2x45^{4+2-1} = 2 (mod 12)
You only have to do 3 calculations like this I think
strange pendant
**Beth**
I do know the extended Euclidean algo
2x17^2 + 2x45^{4+2-1} = 2 (mod 12)
I got stuck here ^
toxic flax
😢
twin salmon
2x17^2 + 2x45^{4+2-1} = 2 (mod 12)
But you aren’t stuck you are done
$0 \leq 2 < 12$
boreal girderBOT
Beth
strange pendant
Well, nothing. You have then shown 2 is not a solution
How does it happened
twin salmon
2x17^2 + 2x45^{4+2-1} = 350 (mod 12)
Your calculation here
Since $350 \equiv 2 \mod 12$
boreal girderBOT
Beth
strange pendant
Can't we simplify until we get a clear contradiction
twin salmon
Can't we simplify until we get a clear contradiction
This is a clear contradiction lol, if 12 divided the sum
twin salmon
If 12 divides this then the remainder is 0
Precisely
strange pendant
2x17^2 + 2x45^{4+2-1} -374 + 24 = 0 (mod 12)
2x17^2 + 2x45^{4+2-1} = 350 (mod 12)
2x17^2 + 2x45^{4+2-1} = 2 (mod 12)
How is this a contradiction
twin salmon
So then 2 = 0 (mod 12). This implies 12|(2 - 0)
By definition a = b (mod n) iff. n|(a - b)
strange pendant
I think you are skipping some steps here
Because i find it hard to fill the gaps
There's nothing wrong with that
Is just that we are out of sync
@twin salmon
twin salmon
By definition a = b (mod n) iff. n|(a - b)
Do you know this definition?
twin salmon
2x17^2 + 2x45^{4+2-1} -374 + 24 = 0 (mod 12)
Look at this passage that you wrote please
strange pendant
I mean
strange pendant
2x17^2 + 2x45^{4+2-1} -374 + 24 = 0 (mod 12)
twin salmon
Do you see 2 = 0 (mod 12)
twin salmon
2x17^2 + 2x45^{4+2-1} = 2 (mod 12)
This is true
twin salmon
17^2 + 45^5 = 1 (mod 6)
Why are we writing this?
strange pendant
I am trying to get to a clear contradiction
twin salmon
Do you see 2 = 0 (mod 12)
Try to see this. Remember a = b (mod n) is an equivalence relation
twin salmon
I am trying to get to a clear contradiction
Your clear contradiction is there
Does 12|2?
elfin finch
Equate the rhs to one another
The left hand sides arent equal to eachother btw
twin salmon
Because that is the clear contradiction
strange pendant
I don't think I follow
elfin finch
And the -374?
twin salmon
And the -374?
It was not my idea to do proof by contradiction
strange pendant
350 = 2 (mod 12)
What about it
2x17^2 + 2x45^{4+2-1} -374 + 24 = 0 (mod 12)
2x17^2 + 2x45^{4+2-1} = 2 (mod 12)
,calc 2-374+24
boreal girderBOT
Result:
-348
,calc 348/12
boreal girderBOT
Result:
29
@twin salmon
compact pewterBOT
@strange pendant Has your question been resolved?
woven plover
Hi
woven plover
I have a chemistry doubt about redox reactions
How does one balance this equation?
<@&286206848099549185>
thorny heath
do you know half reaction
woven plover
Yup
And i tried it
I got MnO4- to Mn3O4
But im stuck at Mn2+ to Mn3O4
wait nvm i got it
.close
still narwhal
how can i simplfiy this thing to the required form
compact pewterBOT
how can i simplfiy this thing to the required form
@still narwhal Has your question been resolved?
uneven wolf
try to integrate the derviative maybe? using a sub like u = tanx/2?
still narwhal
try to integrate the derviative maybe? using a sub like u = tanx/2?
the doctor wants the proof with derviating the normal function
compact pewterBOT
@still narwhal Has your question been resolved?
compact pewterBOT
@still narwhal Has your question been resolved?
still narwhal
yo bro ur smart but i dont understand this part
misty wind
yo bro ur smart but i dont understand this part
Like this
Shouldn't have skipped too many steps sorry
Hope this helps
still narwhal
here bro i dont understand where u got the 2ak and how did u remove 1 from it pls explain it we are almost there
misty wind
here bro i dont understand where u got the 2ak and how did u remove 1 from it pl...
k^2+1=2ak as I have shown in my first page
It's boxed right there
misty wind
here bro i dont understand where u got the 2ak and how did u remove 1 from it pl...
Also for the second part 1-p/q is same as saying (q-p)/p
still narwhal
k^2+1=2ak as I have shown in my first page
oh so k^2 u removed it oh i see now
still narwhal
Also for the second part 1-p/q is same as saying (q-p)/p
but here u didnt change anything upthere in the next step
misty wind
but here u didnt change anything upthere in the next step
Not sure if my handwriting is bad
But it went from 2ck-2 to 2ak-2
c is shorthand for cos
still narwhal
Not sure if my handwriting is bad
But it went from 2ck-2 to 2ak-2
ohhh
bro fr ur really smart
misty wind
Nice flattery
still narwhal
fr but what unvi are u in
misty wind
Not in uni rn I'm in school
compact pewterBOT
Available help channel!
quartz yoke
yooo
quartz yoke
i need help with something
if i have a system of equations and i do elemination method (RREF), and i get a single value for each variable then i have my solution, which is a point
if my intersection is a line by 2 planes, how do interpret my solution when im done doing RREF
weak cobalt
Context?
compact pewterBOT
@quartz yoke Has your question been resolved?
quartz yoke
Need to show this
compact pewterBOT
Need to show this
quartz yoke
i understand we can use this relation but now sure how
status 1
oh
P_n (x) represents the legendre polynomial
please ping
compact pewterBOT
@quartz yoke Has your question been resolved?
quartz yoke
<@&286206848099549185>
compact pewterBOT
@quartz yoke Has your question been resolved?
timid lodge
Need to show this
looks like a classic use of integration by parts to me, did you try that
notice that if you can somehow reduce the legendre polynomial P_n+1 to P_n-1 you can use the inner product property
and integrating the nth derivative provides you with the (n-1)th derivative
quartz yoke
notice that if you can somehow reduce the legendre polynomial P_n+1 to P_n-1 you...
whats inner product property ?
timid lodge
oh just this
quartz yoke
looks like a classic use of integration by parts to me, did you try that
took x^2 for differentiation and P_n+1 (x) and P_n-1 (x) for Integration
the integrations are just piling up
timid lodge
took x^2 for differentiation and P_n+1 (x) and P_n-1 (x) for Integration
I would maybe try taking x^2 P_n-1(x) for differentiation
quartz yoke
notice that if you can somehow reduce the legendre polynomial P_n+1 to P_n-1 you...
its getting very big :P
P_n+1 (x) in terms of P_n-1 (x)
quartz yoke
I would maybe try taking x^2 P_n-1(x) for differentiation
let me try
even then we are having integrations piled up for P_n+1 (x) and also differentiations for P_n-1 (x)
or im just doing it wrong
e
timid lodge
I did what I suggested and it isn't pretty but you do get somewhere
quartz yoke
yea
timid lodge
theres probably an easier way but it seems to be working
induction could work but it would still be ugly lol
quartz yoke
i think i will just move on to bessels and come ot this later
quartz yoke
induction could work but it would still be ugly lol
😭 🙏
i will back to this later
thanks for helping!
timid lodge
i think i will just move on to bessels and come ot this later
when you do come back to it, there is a point in IBP where an integral repeats itself, so you need to do the whole "add it to both sides and divide by 2" trick if you're familiar
but good luck with the other stuff
quartz yoke
when you do come back to it, there is a point in IBP where an integral repeats i...
yea im familiar with it
compact pewterBOT
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Available help channel!
zealous lily
hello I had some question hoping someone answers or correct me if I'm wrong
- Which calculation provides a measure of variability that is expressed in the same units as the original industrial data (e.g., kg, cm, psi)?
a. Mode
b. Variance
c. Mean
D. Standard Deviation
My answer:
— Mean / either Standard Deviation
( standard deviation and mean for me, have the same units as the original data..
- A quality control technician measured the diameter (in mm) of five ball bearings: 10.1, 10.5, 10.3, 10.2, 10.4. What is the mean diameter of these ball bearings?
Mean
= 10.1+10.5+10.3+10.2+10.4
—————————————
5
= 51.5
——–
5
= 10.3 mm
- A manufacturing process has an average yield of 95%. If the standard deviation of the yield is very high, what is the industrial implication?
A. The mean yield is likely incorrect.
B. The process is unstable, with yields fluctuating widely around 95%.
C. The process is highly reliable and predictable.
D. The median yield is a better measure of central tendency.
My answer in this is B. Am I right?
- The maximum load (in kN) tested for five steel cables are: 105, 102, 110, 108, 105. What is the range of these maximum loads?
- 105 kN
- 8 kN
- 5 kN
- 110 kN
Range is where we minus the maximum value to its lowest value of the given answer so that makes it
110 - 102 = 8 or 8kN
- The daily number of defective parts produced by a machine over five days were: 8, 5, 12, 5, 10. What is the mode of this data set?
- 8
- 5
- 10
- 12
Ans - 5
- Which measure of central tendency is the most appropriate to describe the typical cycle time of a manufacturing process when the data is heavily skewed by a few extremely long cycle times due to rare machine failures?
- Standard Deviation
- Mode
- Mean
- Median
Answer: Median
compact pewterBOT
hello I had some question hoping someone answers or correct me if I'm wrong
1....
runic creek
Mean does not show variability
For number 1, there's also very many answers
Iqr, standard dev., range
For 3 yes, the answer is B
I'd really prefer it if you just send another message instead of continually editing one message
zealous lily
I'd really prefer it if you just send another message instead of continually edi...
oh okay sorry
zealous lily
- The flow rate (in L/min) of five hydraulic pumps are measured as: 20.0, 20.2, 19.8, 20.0, 20.5. What is the standard deviation of this flow rate data (rounded to three decimal places)?
- 0.060 L/min
- 0.500 L/min
- 0.353 L/min
- 0.245 L/min
No answer. I'm confused in this part
- In industrial quality control, a smaller standard deviation for a critical dimension suggests which of the following about the manufacturing process?
- The mean dimension is increasing over time.
- The process is less precise and has more variation.
- The process is more stable and the products are more consistent.
- The range of the dimension measurements is larger.
Answer: c
- A set of waiting times (in minutes) for assembly line maintenance tasks is: 15, 12, 18, 10, 20. What is the median waiting time?
- 16 minutes
- 10 minutes
- 15 minutes
- 18 minutes
Answer: C
10.A critical equipment monitoring system, the mean temperature is 150^{\circ}\text{C}. If the standard deviation is 0.5^{\circ}\text{C}, and the control limits are set at {:(),(pm3):} standard deviations from the mean, what is the upper control limit for the temperature?
- $153.0^{\circ}\text{C}$
- $151.5^{\circ}\text{C}$
- $151.0^{\circ}\text{C}$
- $150.5^{\circ}\text{C}$
Answer:
- Two batches of material
were tested for tensile strength (in MPa): Batch A: 310, 312, 308, 311, 309 (Mean = 310 MPa). Batch B: 300, 320, 290, 330, 310 (Mean = 310 MPa). Which statement is true regarding the variability?
- Batch A has a larger standard deviation than Batch B.
- Batch B has a larger standard deviation than Batch A.
- Batch B has a smaller range than Batch A.
- Both batches have the same standard deviation.
Answer: B
- In an industrial process, which measure of central tendency is most sensitive to extreme outliers, such as a single, unusually long equipment downtime?
- Mean
- Mode
- Median
- Range
Answer: median? Or mean?
boreal girderBOT
besh
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
runic creek
Do you remember the formula for the standard deviation?
8,9 correct
What does "pm3" mean in number 10?
11, I don't have pen and paper with me rn, too lazy to check
12, mean is always more sensitive to outliers than median. This is also related to number 6
compact pewterBOT
@zealous lily Has your question been resolved?
zealous lily
What does "pm3" mean in number 10?
thats what written in the Google form. What was put in the Google form, it is what it is. And our teacher aren't that much updated online to answer our questions
runic creek
Do you know what it is tho?
zealous lily
Do you remember the formula for the standard deviation?
Yes, I've done the calculation but it seems wrong
runic creek
Yes, I've done the calculation but it seems wrong
Show a photo of your calculations
zealous lily
Do you know what it is tho?
nope this topic is yet to be discussed 🥹😅
runic creek
nope this topic is yet to be discussed 🥹😅
Without context I absolutely have no idea what pm3 means, so I can't help
runic creek
Show a photo of your calculations
Btw please do this first so I can help
zealous lily
does the photo already sent?
zealous lily
Show a photo of your calculations
runic creek
The five hydraulic presses are not a sample, they are the whole data. So denominator is 5 instead of 4
zealous lily
The five hydraulic presses are not a sample, they are the whole data. So denomin...
right, I just followed what was shown in the ppt 😅 since the denominator n - 1
runic creek
Also, standard deviation is $\frac{(20-\mu)^2 + (20,2-\mu)^2+ etc}{5}$
boreal girderBOT
Matcha
runic creek
Square rooted
compact pewterBOT
runic creek
right, I just followed what was shown in the ppt 😅 since the denominator n - 1
Oh, we're you not taught that it should be just n if the data is not a sample?
.reoepn
.reopen
compact pewterBOT
✅ Original question: #help-43 message
zealous lily
Oh, we're you not taught that it should be just n if the data is not a sample? <...
no not really, this was more like a surprise quiz 😅
runic creek
no not really, this was more like a surprise quiz 😅
Ah i see
Well you should keep that in mind
Try to redo the calculation now
I also noticed that you haven't calculated the mean, remember that that's always the first step to calculating an s.d
compact pewterBOT
@zealous lily Has your question been resolved?
zealous lily
Also, standard deviation is $\frac{(20-\mu)^2 + (20,2-\mu)^2+ etc}{5}$
so I have to written it like that?
runic creek
so I have to written it like that?
Wdym?
Your mistake is that you summed the data points' squares instead of the data points' difference from the mean's squares
zealous lily
Your mistake is that you summed the data points' squares instead of the data poi...
from data points difference you mean sample variance right?
runic creek
from data points difference you mean sample variance right?
Can you explain what you meant
I don't get what you are saying
zealous lily
Can you explain what you meant
I mean like solve solve it one by one or not... I'm confused
compact pewterBOT
compact pewterBOT
Available help channel!
slim ember
If I prove XE parallel to AD, I am done
But I am not able to do that
compact pewterBOT
If I prove XE parallel to AD, I am done
But I am not able to do that
@slim ember Has your question been resolved?
compact pewterBOT
@slim ember Has your question been resolved?
covert spear
No idea how to find the partial sum
compact pewterBOT
No idea how to find the partial sum
kind crane
you should keep the sum as 1 sum of a difference
write out a few terms of 1/(n+2) - 1/(n+3) say for n = 0, 1, 2, 3 and find a pattern
boreal girderBOT
Bakoles
covert spear
cause all the middle terms kinda disappear
solemn wasp
No idea how to find the partial sum
you can reindex one of the sums so that the junk you're adding in each looks the same
that way you can take some terms out of each, so you get outliers(n) + sum(a_n - a_n)
covert spear
you can reindex one of the sums so that the junk you're adding in each looks the...
i don't really get it
change n = 1 for the 1/(n+2)?
or what did you mean by index
solemn wasp
$\sum_{k=0}^na_k-\sum_{k=0}^na_{k+1}=\sum_{k=0}^na_k-\sum_{k=1}^{n+1}a_k$
boreal girderBOT
Flip
solemn wasp
see? the junk in each is the same, so you can take out some of the first/last terms so that the sums are exactly equal, so their difference is 0
solemn wasp
it helps make telescoping series more obvious, especially if they're not just 1 apart like this
idc, choose what you like
covert spear
okay i'll try your way
solemn wasp
if you can see it, great
covert spear
ohhh
the first sum is basically 1/2 + the second one
so if we get a difference of equal sums
the only thing left is 1/2
i think i get it
I tried it for the second one
is this the way you meant?
main pendant
I tried it for the second one
Wait, when you re-index the sum, you have to look carefully at what you are summing.
main pendant
I tried it for the second one
The sum of 1/(3n + 1) from n = 0 to infinity means you are summing:
1/1 + 1/4 + 1/7 + 1/10 + ...
The way you reindexed the sum was that you changed 1/(3n + 1) to 1/(3n - 2). In particular, you started from n = 3. Can you tell me what this sum would look like if you started summing from this index?
main pendant
Exactly.
The main problem with your new sum is where your new sum starts. Instead of n = 3, where should it start at?
main pendant
n = 1?
Perfect.
Indeed, n = 1 works, and you can confirm it when you substitute it in.
main pendant
No problemo :)
covert spear
.close
compact pewterBOT
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Available help channel!
rough fjord
quick question
compact pewterBOT
quick question
rough fjord
how do we go from 2 to 3?
rough fjord
ok thanks
the image I provided shows "x = 1/y" the in step 2 says That equation describes the inverse?
how come?
kind crane
1/(1 / something) = something
alternatively, you can prove that with exponent rules
$\lp x^\inv\rp^\inv = x^{(-1)(-1)} = x^1$
boreal girderBOT
riemann
compact pewterBOT
@rough fjord Has your question been resolved?
compact pewterBOT
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Available help channel!
quartz imp
can anyone help with this? "i" isnt a varible its an imaginary number
compact pewterBOT
can anyone help with this? "i" isnt a varible its an imaginary number
solemn matrix
can anyone help with this? "i" isnt a varible its an imaginary number
do you know what $i^2$ is?
boreal girderBOT
1 divided by 0 equals Infinity
quartz imp
do you know what $i^2$ is?
no i dont. we learned this in algebra 2 yesterday and i havent got it
solemn matrix
$i$ is the imaginary number where $i = \sqrt{-1}$
boreal girderBOT
1 divided by 0 equals Infinity
solemn matrix
now from that, do you know what $i^2$ is?
boreal girderBOT
1 divided by 0 equals Infinity
hardy delta
$n=\left(\sqrt{n}\right)^2$
boreal girderBOT
The Star
hardy delta
because it will made it positive
Does this help?
quartz imp
what is $n$
boreal girderBOT
jared!
hardy delta
what is $n$
Any number
hardy delta
Importantly, n can be complex or imaginary too
quartz imp
why is it in paratheses
hardy delta
it is not limited by reals
hardy delta
why is it in paratheses
to make it clear that im doing sqrt first, then squaring
quartz imp
im still lost
hardy delta
you can write it without doing that but the brackets help you see what is being done first
hardy delta
**The Star**
$i^2=\left(\sqrt{-1}\right)^2$
boreal girderBOT
The Star
hardy delta
Does this make sense?
quartz imp
why does it become -1
hardy delta
sqrt is the inverse function of squaring a number. taking a sqrt of a squared number gives back the principal value of the number originally squared
hardy delta
why does it become -1
Because $i=\sqrt{-1}$
boreal girderBOT
The Star
quartz imp
rhs?
quartz imp
ok
hardy delta
can anyone help with this? "i" isnt a varible its an imaginary number
Now you should be able to use basic exponent laws, yes?
quartz imp
**1 divided by 0 equals Infinity**
so this is -1?
solemn matrix
so this is -1?
yes
hardy delta
yup
solemn matrix
can anyone help with this? "i" isnt a varible its an imaginary number
now can you write $i^{66}$ as $(i^2)^{something}$?
boreal girderBOT
1 divided by 0 equals Infinity
quartz imp
its subtracing 1 from the 66 until we get to a perfect square right?
solemn matrix
its subtracing 1 from the 66 until we get to a perfect square right?
wdym?
hardy delta
its subtracing 1 from the 66 until we get to a perfect square right?
nope
quartz imp
some kid did it that way in class idk
solemn matrix
**1 divided by 0 equals Infinity**
use some basic exponent laws to answer this
quartz imp
bro the teacher lets him teach some times bro hes so smart😭
hardy delta
$\left(a^{m}\right)^{n}=a^{(mn)}$
boreal girderBOT
The Star
hardy delta
Ever seen this?
quartz imp
-1 to the 66th power?
solemn matrix
**The Star**
it's weird to put the exponents in the parentheses
quartz imp
Ever seen this?
no
hardy delta
it's weird to put the exponents in the parentheses
rhs? thats a typo lmao but doesnt really matter xD
solemn matrix
why is the kid teaching complex numbers
solemn matrix
rhs? thats a typo lmao but doesnt really matter xD
let this guy come to your school and kick that kid out
quartz imp
bro hes way ahead of us
hardy delta
your teacher is way ahead of him
bro is on paid vacation 😭
quartz imp
im in 9th grade but taking 11th grade math (algebra 2 trig HN) my parents made me
so math is kinda hard
solemn matrix
im in 9th grade but taking 11th grade math (algebra 2 trig HN) my parents made m...
☠️
JUST GO OVER
YOUR
CURRICULUM
NOT LEARNING 11TH GRADE MATH
😭
hardy delta
<@689406988782010388> wtf is wrong with the kid teaching him
idk 😭
quartz imp
will u guys be on in 30-45 mins?
solemn matrix
np
hardy delta
will u guys be on in 30-45 mins?
yes
POV: youre waiting for someone to explain math so you go and help others instead
totally not me
quartz imp
also im running dc on an unblocked school chromebook so its hard to be on
solemn matrix
@quartz imp do you see this?
https://discord.com/channels/268882317391429632/903481102591750184
hardy delta
<@1332159452417233008> do you see this?
https://discord.com/channels/26888231739...
why is bro scaring him 😭
solemn matrix
this is to prove @hardy delta is more advanced than the kid teaching you
hardy delta
this is to prove <@689406988782010388> is more advanced than the kid teaching yo...
I would hope so since I graduated 😭
solemn matrix
😭
solemn matrix
I would hope so since I graduated 😭
this is to prove that YOU are more advanced than the kid that teaches @quartz imp
compact pewterBOT
@quartz imp Has your question been resolved?
compact pewterBOT
compact pewterBOT
Available help channel!
ionic ermine
compact pewterBOT
winged lion
,rccw
boreal girderBOT
compact pewterBOT
@ionic ermine Has your question been resolved?
winged lion
u literally just posted some snippet
untold compass
@wild pivot
ionic ermine
u literally just posted some snippet
wym
winged lion
it would help to describe your problem/question, what you tried and your progress is
ionic ermine
that's the thing every approach i could think of lead to almost nothing
I'd say try inclusion-exclusion
solemn wasp
I'm suspicious about the problem
it's multiple choice, and that lessens the workload substantially
ionic ermine
bro so you wanna put small values of n and verify?
cerulean steeple
say the intersextion of A and B is D, and C and B is E, what if you choose two disjoint subsets of X to be D and E, then the rest of the elements you can assign to only one of A,B,C. doesent this create the triplets?
ionic ermine
there's another case
where you have elements common in both intersections but none common with AintersectionC
cerulean steeple
yeah thats why you choose disjoint subsets from the X to be D and E, since if theres something in DintE, then theres something in AintBintC
ionic ermine
oh i see
cerulean steeple
although this has some wierd sum, so maybe this wouldnt work out
solemn wasp
is "2.5^n" denoting 2 times 5^n, or (2 + 1/2)^n?
idk why I just believed it was the latter
cerulean steeple
i mean logically its the first
solemn wasp
yeah but, that's not how I write it, and I believed this could be like a silly gotcha
ionic ermine
although this has some wierd sum, so maybe this wouldnt work out
bro
you just solved it
it isn't a wierd sum
cerulean steeple
it isnt?
boreal girderBOT
cerulean steeple
that works?
cerulean steeple
what did you define A', B', C' as?
ionic ermine
the rest of the set after removing the intersection
compact pewterBOT
cerulean steeple
the "wierd sum" i was refering to was this (which wasnt even correct in the end 
ionic ermine
no you just didn't think of inclusion exclusion, most people don't at first
compact pewterBOT
Available help channel!
civic crescent
if i want to integrate 1/(1-u) i took out the negative and wrote it as -1/(u-1) then =-Ln|u-1| but the correct answer is -Ln|1-u| what is wrong here
compact pewterBOT
if i want to integrate 1/(1-u) i took out the negative and wrote it as -1/(u-1) ...
civic crescent
.close
compact pewterBOT
daring axle
if i want to integrate 1/(1-u) i took out the negative and wrote it as -1/(u-1) ...
nothing?
compact pewterBOT
Available help channel!
wintry knot
for such type of questions, is there a way to calculate them directly rather than drawing each subgraph?
compact pewterBOT
for such type of questions, is there a way to calculate them directly rather tha...
oak path
in general, no, but in this particular case its very easy because of symmetry and small size
wintry knot
yeah, but what if we had, say, W7 or something?
compact pewterBOT
Please don't repeatedly close and claim a new channel with the exact same question. This erases all previous progress made towards your problem and is confusing for helpers, making it more difficult to help you. Please be patient, even if your channel has not received much attention.
thorny heath
Please don't repeatedly close and claim a new channel with the exact same questi...
i meant you can keep previous channel open
wintry knot
it would not pin my current question
thorny heath
it would not pin my current question
k
oak path
generally speaking, any graphs for which there are names for that aren't highly irregular and weird it will be pretty easy for
oak path
any issues in getting that answer?
wintry knot
not particularly, but it was still a bit tedious. since we have a time constraint in the examination and there's a possibility that we could get a question with a more complicated graph, i was just wondering if we could somehow use p&c here? it might be just me though who is finding it kinda hard
oak path
yeah general combi approaches here can make things easier
you just have to apply your experience and hope its enough to make the problem tractable
immediate intuition for me is to separate cases by number of vertices
then split subcases by number of edges
compact pewterBOT
compact pewterBOT
Available help channel!
upbeat pond
Carol is walking home from school along a path. She sees a dog that is 40 feet away, and her line of sight makes an angle of 20° with the sidewalk. The dog's leash is 25 feet long. What length of the sidewalk should Carol avoid to remain safe from the unknown dog?
I don’t understand how to sketch this.
Can someone sketch this diagram for me?
compact pewterBOT
Carol is walking home from school along a path. She sees a dog that is 40 feet a...
@upbeat pond Has your question been resolved?
upbeat pond
<@&286206848099549185>
There are 300k people in this server and yet no one wants to help me 💀
chilly parcel
There are 300k people in this server and yet no one wants to help me 💀
Is that exactly how the original problem is formulated? No diagrams? 😭
Because "sees a dog that is 40 feet away" is ambiguous to me, is it from the eyes or from the feet? Where is the leash connected to?
upbeat pond
Is that exactly how the original problem is formulated? No diagrams? 😭
Yes it is
upbeat pond
Because "sees a dog that is 40 feet away" is ambiguous to me, is it from the eye...
I’m asking the same questions idk man
chilly parcel
I’m asking the same questions idk man
well i'd assume it's from the eyes because they gave an angle, so you can use trigonometry
and I'd also assume the leash when pulled taut is parallel to the ground
upbeat pond
They only gave an angle between the eyes of Carol and the sidewalk, not the dog
chilly parcel
but it's a badly written question though lol
chilly parcel
They only gave an angle between the eyes of Carol and the sidewalk, not the dog
yeah I know
upbeat pond
but it's a badly written question though lol
The previous question is even worse lol
compact pewterBOT
@upbeat pond Has your question been resolved?
toxic cipher
Carol is walking home from school along a path. She sees a dog that is 40 feet a...
Are you absolutely sure this is the problem word for word? If you had a picture of the original problem that would be nice.
Even if the problem was originally in another language, still post it
toxic cipher
This question is badly written.
toxic cipher
The previous question is even worse lol
can you show the previous question so that I can maybe try to understand what your teacher is on
upbeat pond
This question is badly written.
So is this one
It’s like ”The sun is at least two meters away from earth. How many apples does Jim have?”
toxic cipher
you can ping helpers, maybe someone else will understand the question
compact pewterBOT
tired bear
hold on
tired bear
So is this one
this seems to somewhat match the description
upbeat pond
this seems to somewhat match the description
So what are we trying to figure out?
tired bear
from the first section of the question you find the distance of the camera from the sidewalk
using trigonometry
and then find the length of sidewalk covered using pythagorean theorem
since we know one of the sides (d) and hypotenuse (22 m)
tired bear
this seems to somewhat match the description
the question seems to be asking for the 'l' marked in this diagram
upbeat pond
this seems to somewhat match the description
But the angle of 22 is indefinite because it is a circle radius?
tired bear
But the angle of 22 is indefinite because it is a circle radius?
no i forgot to complete the circle
its a full circle
thats a weird way to put it
compact pewterBOT
✅ Original question: #help-43 message
upbeat pond
Omg my PC got a BSoD mid-drawing 😂
@tired bear
Notice how they're all 22
So there is no definite angle for 22 perpendicular to the flat line between the eye and the camera
So therefore I don't see how you can have an $l$ variable if we can't measure it
boreal girderBOT
Elliot Pixel
upbeat pond
<@&286206848099549185>
tired bear
<@702550180154834984>
wait up
can you understand the second diagram i drew
the one with the policeman and the camera
the line joining them making a 38 degree angle with the sidewalk
upbeat pond
Yes, although shouldn't 38 be this angle?
tired bear
"a police officer can see the camera at an angle of 38 degrees with the sidewalk"
meaning with a line along the sidewalk
the line you are showing is perpendicular to the sidewalk
a sidewalk goes along the road
upbeat pond
Wait lemme just put the question here so we have it
A crime was committed at a store on Main Street. A security camera is found across the street, and police are doing an investigation. When standing on the sidewalk, a police officer can see the camera at an angle of 38° with the sidewalk, and the camera is 30 m away. If the camera can pick up images up to 22 m away, what length of the sidewalk would be visible in video footage to help solve the crime? Include a diagram in your solution.
Gosh this is confusing
I think you're right tho
upbeat pond
Yeah that would just be $sin(38 \textdegree)=\frac{d}{30}$
Let me check if that's the right answer
boreal girderBOT
Elliot Pixel
tired bear
we havent gotten to the answer yet
upbeat pond
there is an answer sheet
oh you mean like that
So we need to subtract 22 from that?
So $30sin(38)-22$
upbeat pond
Yes
tired bear
it is given that the camera can notice anything upto a distance of 22 m
boreal girderBOT
Elliot Pixel
tired bear
so you can only see a part of the sidewalk from the camera due to that restriction
upbeat pond
Jeez what am I doing atp
upbeat pond
so you can only see a part of the sidewalk from the camera due to that restricti...
Yes
tired bear
the question is asking for the length of the sidewalk that is visible from the camera
this basically becomes a question of finding the length of a chord
given its distance from the center and the radius of the circle
upbeat pond
So what values do we know of the chord?
tired bear
this is what weve determined upto now
upbeat pond
And l is just twice of the triangle's side
upbeat pond
So Pythagorean theorem:
$a^2+b^2=c^2 \Rightarrow b^2=c^2-a^2 \Rightarrow b^2=22^2-(30sin(38))^2 \Rightarrow b \approx 11.95260863$
$2 \cdot 11.95260863 \approx 23.91 m$
tired bear
yup
boreal girderBOT
Elliot Pixel
upbeat pond
Awesome
Let me think this through for a sec
This question baffles me so much idk why
@tired bear
What am I missing in my diagram
tired bear
<@702550180154834984>
thats not 38 degrees with the sidewalk
maybe you can draw the sidewalk the policeman is walking on
tired bear
cool
upbeat pond
The problem is that I don't see how I can algebraically connect the radius of the circle to the triangle
Like they don't seem to correlate whatsoever
tired bear
22 m should be a bit larger than that
since 30sin(38 deg) (side of the red triangle) is less than 22
tired bear
the best thing to do is to not draw both diagrsms together
first draw the diagram where the police is walking on the sidewalk and looks at the camera
and THEN draw a new diagram separately for the circle surrounding the camera along with the sidewalk
tired bear
"when standing on the sidewalk, a police officer can see the camera at an angle of 38 degrees with the sidewalk, and the camera is 30 m away."
ONLY this part
not the 22 m one
the sidewalk, the police officer and the camera
with whatever else you need to construct on it
tired bear
the sidewalk
tired bear
you dont need to consider any height differences
just consider the birds eye view
its difficult to draw from a second persons view
like how you view something from the top at google maps
upbeat pond
just consider the birds eye view
tired bear
bingo
tired bear
2d
i dont think they want you to consider everything in 3d
its too difficult
in real life problems either side view or birds eye view makes sense in the context of questions like these
birds eye in this case
upbeat pond
but you cant draw the slope from the police's eyes to the camera with bird's eye?
upbeat pond
thanks
tired bear
you get a tilted right triangle
not very promising
if their heights are the same then we're back to birds eye
upbeat pond
But what I'm trying to understand is how the circle's radius is able to correlate to the triangle
@tired bear
tired bear
you cant correlate the circle with THIS triangle
you need this triangle just to find the distance of the camera from the sidewalk
which adds to the next part of the question
tired bear
What exactly is 30 sin(38)
distance of the camera from the sidewalk
the centre of the circle is the camera
compact pewterBOT
tired bear
gn
compact pewterBOT
Available help channel!
carmine garden
If a linear transformation $E$, is such that $E=E^2$. And $\norm{Ex}≤\norm{x}$ . show $E=E^*$
compact pewterBOT
If a linear transformation $E$, is such that $E=E^2$. And $\norm{Ex}≤\norm{x}$ ....
boreal girderBOT
wai
carmine garden
I'm not sure how to use the unequality here
$\langle E^2x,x \rangle = \langle Ex, E^*x \rangle. = \langle Ex,x \rangle$
boreal girderBOT
wai
carmine garden
.close
compact pewterBOT
compact pewterBOT
Available help channel!
thick shore
Can anyone help me on ts
compact pewterBOT
Can anyone help me on ts