#help-23
stoic dune
Ye. That's what they did
stoic dune
Just, instead of calling it x, call it a•b
dense hedge
dont i technically know a and b
if i plugged in 1 for both
or why did he plug in 1 for both
lean otter
a and b are unit vectors
stoic dune
He did plug in |a|² = 1 and |b|² = 1
dense hedge
yea
stoic dune
Yeah, I assume that the question states somewhere that a and b are unit vectors
lean otter
a is a vector |a| is the norm which is a number
lean otter
the norm is one
stoic dune
u is a unit vector → |u| = 1
dense hedge
ahh
but i still dont understand why -6a vecotr * b vector = -6
is a*b=1
are we just thinking a*b as x?
like idk
and 6 is the coefficent
lean otter
-6(a•b)=-6 => (a•b)=1
stoic dune
-6 times some number = -6
That number must be 1
Don't worry too much about the fact that we call it a•b
lean otter
.close
pure spruce
hi I'm trying to use the limit comparison test to see whether this integral in convergent and divergent but I really don't understand my prof's process
safe radishBOT
hi I'm trying to use the limit comparison test to see whether this integral in c...
pure spruce
I was hoping someone could help me with that
the fact that there's a trig function is confusing as heck
stoic dune
Limit comparison is a different thing
pure spruce
oh you're right
stoic dune
Comparison (or sometimes direct comparison) is what we're going for here
pure spruce
yah I meant that sorry I mixed them up
stoic dune
Think instead about
∫ 9 / (x² + 1) dx
pure spruce
why do I think about it like that
stoic dune
Because |cos²(x)| ≤ 1
So the magnitude of my integral is greater than the magnitude of yours
pure spruce
hmm ok lemme think about it for a little bit
@stoic dune sry you still there
I was wondering how you compare the 2 like how do you decide which one is greater
well I can compare it to 9/x^2 right
ok this one is a little more confusing because I know 10 / x+e^(2x) is less than 10/x but that doesn't prove anything because 10/x is divergent between those bounds
it's hard to wrap my head around lol
safe radishBOT
@pure spruce Has your question been resolved?
safe radishBOT
safe radishBOT
Available help channel!
pure spruce
safe radishBOT
pure spruce
how would I approach using the comparison test in this problem
plucky elk
is that an exam?
pure spruce
No it’s online hw
It’s a site called webworks
Exams are wayy easier
He makes the hw hard for us
light shoal
hint: for small x, sin(x) is approximately equal to x
light shoal
no you can't, you need to examine its behavior near x=0
since that's the only place where the denominator can be problematic
pure spruce
But that’s why I take the limit tho right
pure spruce
Couldn’t I just compare it to a function like 1/x^2
light shoal
sure, if you can justify that comparison
that's why i suggested using that sin(x) is approximately x for small x
(actually it suffices to simply use sin(x) <= x for x >= 0)
pure spruce
But sin(x) just goes between one and -1 how does it have anything to do with the x term by itself
pure spruce
I thought the problem with this type of question is that I can’t easily or maybe even possibly integrate it so I have to find an alternate function to take advantage of the comparison theorem
plucky elk
you can show an integral diverges using the comparison test
light shoal
I thought the problem with this type of question is that I can’t easily or maybe...
for small x > 0 we have 0 < sin(x) <= x, and therefore 1/sin(x) >= 1/x...
pure spruce
for small `x > 0` we have `0 < sin(x) <= x`, and therefore `1/sin(x) >= 1/x`...
Sorry I’m kind of slow to learn this topic and what you’re saying is still a little to abstract for me
light shoal
Sorry I’m kind of slow to learn this topic and what you’re saying is still a lit...
i'm suggesting a comparison to use
pure spruce
Oh you’re suggesting 1/sin(x)
light shoal
yes it's bigger than 1/x for small x
therefore 1/(x sin(x)) is bigger than 1/x^2 for small x
lean otter
Sorry I’m kind of slow to learn this topic and what you’re saying is still a lit...
or just xsinx<=x also works
pure spruce
or just xsinx<=x also works
So does 1/x converge is that what you’re saying
flat frigateBOT
lean otter
so by comparison the original integral must also diverge
pure spruce
Yah I’m just trying to understand because the whole point of finding a similar function is to either make some kind of bound for which I can compre the original to
plucky elk
and
https://tutorial.math.lamar.edu/classes/calcii/ImproperIntegralsCompTest.as...
read this
pure spruce
Oh so this would be one of those instances where I use it to prove it diverges
lean otter
yess
pure spruce
Oh ok yah because sin only goes up to one so at most it would match it
But how would I prove that on a test more formally I feel like the intuition is there but not so much me being able to work it out you know
light shoal
sigh, damn latex
safe radishBOT
@pure spruce Has your question been resolved?
hushed mirage
i have a computer graphics related question
safe radishBOT
i have a computer graphics related question
hushed mirage
the "normals" of a triangle's vertices are interpolated on its surface
this is usually not to represent the actual normal of the triangle, but a rounder looking surface
as the normal is used to calculate shading
im wondering what kind of shape the normals actually represent?
i think its most likely paraboloid like shape as that seems to be the case for a right angle triangle
safe radishBOT
@hushed mirage Has your question been resolved?
split trench
Consider the function f(x)= x^4/625. If f^-1 is the inverse of f(x), find f^-1(625)
It's x^4/625 since that is its inverse form?
safe radishBOT
Consider the function f(x)= x^4/625. If f^-1 is the inverse of f(x), find f^-1(6...
thin token
split trench
What formula is that?
fiery remnant
f(x)= x^4/625
Replace f(x) with y
y=x^4/625
Make x the subject
625y=x^4
x=4√625y
Replace x with f^-1(x) and y with x
f^-1(x)=4√625x
f^-1(625)=+-4√625(625)=+-25
hope this helps
get someone to confirm that this is correct
fiery remnant
get someone to confirm that this is correct
@thin token
split trench
.close
kind dove
safe radishBOT
solar coral
Hello I’m in year 10 and need help with factorising, I’ll send I’m my question below
safe radishBOT
Hello I’m in year 10 and need help with factorising, I’ll send I’m my question b...
solar coral
1.a
tame edge
15e-10, what kind of factor do they have in common?
solar coral
1, 5? I’m not good at maths aha
tame edge
So you have 15e and -10, since it's only one variable, you are gonna only focus on 15 and -10.
$15$ and $10$, is there something in common that can divide them? And the result is a integer?
tall bough
read #❓how-to-get-help and delete your comments
flat frigateBOT
Potet
safe radishBOT
@solar coral Has your question been resolved?
lean otter
safe radishBOT
fading raft
whats the question
safe radishBOT
@lean otter Has your question been resolved?
elfin willow
a little bit more physics but
safe radishBOT
a little bit more physics but
elfin willow
how do u read this graph
i cant understand it for the life of me
apparently on the y axis, thats ||300,000||
safe radishBOT
@elfin willow Has your question been resolved?
lean otter
as resistance decreases luminosity increase
elfin willow
as resistance decreases luminosity increase
i understand that, i just dont understand the scale on the graph
see like all those lines
lean otter
I assume it's just the intervals changing in how far apart they are. as either axis increases in units
elfin willow
I assume it's just the intervals changing in how far apart they are. as either a...
so you see that red line on the y axis
thats apparently 300,000
how does that work
lean otter
Well you know one line is 10^0 so 10^0x=300,000 so that line is 300,000 because 10^5 is 100,000
civic forum
Hey
safe radishBOT
@civic forum Has your question been resolved?
civic forum
(Please tag me thanks)
safe radishBOT
@civic forum Has your question been resolved?
civic forum
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pine tulip
Isn't the correct thing the one below?
safe radishBOT
Isn't the correct thing the one below?
peak estuary
no because we have multiplication signs and not plus
essentially this is just (ab)(cd)=abcd=acbd=...
pine tulip
but isnt that the whole reason we need to multiply 9 for both 4 and 10^-2?
peak estuary
not with multiplication, no. if it was (9+10^6)(4+10^-2) then yes
pine tulip
oooooh, now i understand
thank you a lot, i didnt understand what you meant the first time 🙂
.close
oblique citrus
Hi! I am trying to understand something. We are trying to find the value of b so that the discriminating factor = 0
safe radishBOT
Hi! I am trying to understand something. We are trying to find the value of b so...
oblique citrus
so the formula of delta = b^2 - 4ac = 0
this is the solution, however I don't understand what is a, b and c here
i originally assumed a = 1
c = -3/4
but what is b = ?
oblique citrus
i originally assumed a = 1
c = -3/4
but what is b = ?
hm i wrote it confusingly. I'm thinking of the b in delta = b^2 - 4ac that is the b of the polynomial, not the actual b we are looking for.
peak estuary
the general quadratic is ax^2+bx+c. so this b in our case is -1
but yeah slightly confusing notation
and the c in our case is b^2-3/4 with the b from the question
to clarify, I will write the question as x^2-x+t^2-3/4
then a=1, b=-1 and c=t^2-3/4
oblique citrus
the general quadratic is ax^2+bx+c. so this b in our case is -1
ohh i understand i was hesitating where should i put b^2
thank you very much
i will complete my exercise now. good day !
.close
mighty frigate
tall bough
?
sharp sage
lean otter
when you see the bar graph
northwest number of departments seems equal to southwest number of departmets
so how many?
safe radishBOT
@mighty frigate Has your question been resolved?
lean otter
mfw getting ignored
mighty frigate
6
or i guess 3 if youre counting the lines by 1
but since southeast is the same then i can infer 6
safe radishBOT
@mighty frigate Has your question been resolved?
mighty frigate
@lean otter
plucky elk
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buoyant nebula
safe radishBOT
harsh sleet
whart?
buoyant nebula
Have you seen the question ?
harsh sleet
Have you seen the question ?
it did not open
peak estuary
I'd rather not download some random data format
harsh sleet
why dont you post the photo?
safe radishBOT
@buoyant nebula Has your question been resolved?
olive sonnet
by each shaded region does the question mean that it wants you to give an answer for each right triangle and the rectangle individually
or just the shaded region as a whole
I'll give an answer either way
for the triangle, the base is 5 units and the height is 4. then, use the formula for a triangle's area to find it (base*height/2) giving you 10 units squared.
for the rectangle, use the formula for the area of a rectangle (length x width), in this case being (5 x 12), giving you 60 units squared
so for each individual, the right triangles are 5 units squared each (the whole triangle is 10) and the rectangle is 60 units squared, so the whole shaded region would be 70 units squared.
buoyant nebula
@olive sonnet thx for the explanation
safe radishBOT
Available help channel!
stable igloo
Does this make sense?
safe radishBOT
Does this make sense?
winter pivot
Yeah
stable igloo
but having a root in 0 with multiplicity 2 isn't weird?
winter pivot
Notice how the constant term is 0
stable igloo
I think I worded that horribly
winter pivot
As well as the linear term
stable igloo
ok thanks, i thought it was wrong because of the multiplicity
winter pivot
Ye
stable igloo
.close
safe radishBOT
safe radishBOT
Available help channel!
gilded wigeon
how do you find the volume of ellipsoid without the width?
safe radishBOT
how do you find the volume of ellipsoid without the width?
@gilded wigeon Has your question been resolved?
Available help channel!
hazy moon
I’m correcting my test to retake it and I’m not sure about these three here
hazy moon
Also the instructions say “Evaluate each limit”
merry sleet
for the 13 and 17 you should know that inf/inf is undefined
like for example
x/x² is inf/inf
but its also equal to 1/x
which approaches 0
hazy moon
one sec
merry sleet
on the other hand
distant trench
inf/inf is not 1
distant trench
you can use factoring here
merry sleet
and x/x is inf/inf and goest to 1
hazy moon
you can use factoring here
I didn't think factoring helped
merry sleet
when in cases like this you should factorize by the most powerful term in both parts of the fraction
in this case
distant trench
I didn't think factoring helped
$\lim_{x \to \infty} \frac{16x}{x^2+16}$
flat frigateBOT
Asagao 朝顔
distant trench
you can do some "illegal" factoring here
hazy moon
so 16x/(x+4)(x+4)
merry sleet
why illegal? just factorize by x² on the bottom
distant trench
no
distant trench
why illegal? just factorize by x² on the bottom
it feels illegal but it's correct
merry sleet
its not illegal at all both expressions are equal for x=/=0
distant trench
there is no factored version of x^2+16
distant trench
it's an irreducible quadratic
hazy moon
oh right
flat frigateBOT
Asagao 朝顔
merry sleet
this is jkust the denominator
hazy moon
huh I've never seen that before
flat frigateBOT
Asagao 朝顔
distant trench
from here it's pretty clear where it's going
$\lim_{x \to \infty} \frac{16}{x(1+\frac{16}{x^2})}$
flat frigateBOT
Asagao 朝顔
hazy moon
it's as it approaches -∞ btw
hazy moon
yeah dw
distant trench
$\lim_{x \to -\infty} \frac{16}{x(1+\frac{16}{x^2})}$
flat frigateBOT
Asagao 朝顔
distant trench
you now have 16/-infty
which is 0
this way of factoring is pretty useful to make sense of this
hazy moon
this is really strange but it works
distant trench
yeah
hazy moon
what about for number 15?
distant trench
do you know what cot is in terms of sin and cos
hazy moon
cos/sin=cot
distant trench
yes
hazy moon
I remember I plugged all of this into my calculator and just wrote the numerb that came out
hazy moon
woudn't it be sin( -5pi/3) bc its 2x
distant trench
uh
remember
when you do that be careful
$-2 \cot (2x) = \frac{-2}{\tan (2x)}$
flat frigateBOT
Asagao 朝顔
hazy moon
ah
distant trench
since cot(x) = 1/tan(x)
you don't flip the -2 with it
the calculator gives you -1.155
$-2 \times \cot (2x) = -2 \times \frac{1}{\tan (2x)}$
flat frigateBOT
Asagao 朝顔
distant trench
you can think of it like this
hazy moon
yeah that makes sense
hazy moon
actually I have a question about this
distant trench
go ahead
hazy moon
so -1.15 is the right answer but the answer key displays it as -2 √(3)/3
distant trench
ohhh
hazy moon
how would I know how to get it from decimal form to fraction form?
distant trench
it wants you to give the exact answer
hazy moon
yeah
hazy moon
unit circle?
hazy moon
yeah mostly
hazy moon
give me a sec I need to write out the rest of the problem first
distant trench
ok
distant trench
ok
distant trench
ok
hazy moon
actually nvm I figured it out
I think I'm good rn
I really appreciate your help internet stranger
.close
floral urchin
safe radishBOT
floral urchin
<@&286206848099549185>
plucky elk
read this
safe radishBOT
@floral urchin Has your question been resolved?
gaunt gyro
safe radishBOT
gaunt gyro
hey I have a quick question
I know the awnser is c. I am just very confused what it means by h(w) gets very large
stoic dune
As the curve goes further left, it also gets very tall
As w approaches 0, H(w) gets very large.
pliant mulch
Is the work i did to get X correct? if thats correct, how would i find Y from there?
safe radishBOT
Is the work i did to get X correct? if thats correct, how would i find Y from th...
pliant mulch
Because the work was on a different sheet i tried to copy my work onto ms paint
unkempt pecan
Is the work i did to get X correct? if thats correct, how would i find Y from th...
not really
quasi bison
no, your work for x is not correct
you cannot just erase y from the equation like you did
quasi bison
subtracting 38 from both sides on line 4 should have left you with 2x = 180 - 38 - y
but also yes what veeral said
pliant mulch
x+7+3x-18+x-9=180
would that equation simplified be 5x - 20 = 180?
unkempt pecan
yeah
indigo trout
My dad is trying to engrave some stuff on mug's and this circular objects are comming off as eggy looking i told him its because of the perceived distance between the sides is smaller because of the curvature of the mug.
I was trying to figure out how to make it so that height of the circular objects being engraved matches the perceived width vs the actual width.
safe radishBOT
My dad is trying to engrave some stuff on mug's and this circular objects are co...
indigo trout
S is circle width that im projecting onto the mug and r is the radius of the mug
this was how i set it up. i wanted to find l which i understand to be the chord length.
i set it up this way because i thought i could use some vector properties and polar cordinates to find L
this is what i came up with. But im not sure if its correct.
winter pivot
L in terms of?
indigo trout
sorry not sure if the print is too small L is the chord length of the arc S
the dashed bit.
indigo trout
S and r are given.
r is the radius of a cylinder (its a mug irl) and S is the diameter of a circle being projected onto the cylinder if that makes sense
winter pivot
Law of cosines would make this a lot easier
$L^2 = ||a||^2 + ||b||^2 - 2||a||b||\cos(\theta_{ab})$
flat frigateBOT
EndTimes
indigo trout
what i drew could be a topdown view of the mug and the red arc length is the the width of a circle that is being ectched onto it.
indigo trout
so the thing is have no theta.
winter pivot
Lucky for you
winter pivot
$\theta_{ab} = S_{ab}/r$
flat frigateBOT
EndTimes
winter pivot
Yep
winter pivot
Everything is good up until u
Everything you do with u is just flat out wrong lmao
You appear to be confusing the Cartesian and polar coordinates systems
indigo trout
maybe so
this is what i had in my head
but i see now i didnt even get it right
where i had P and R right and ||Q|| would be L
or so i thought
winter pivot
Yeah that would work if you performed the vector subtraction correctly
indigo trout
😅
winter pivot
Unfortunately vector addition in polar coordinates isn't really that simple, you have to convert to Cartesian coordinates first
winter pivot
Are you alright with that formula or is there something else you're missing
You defined |a| = |b| = r so it really simplifies nicely:
2r^2 (1-cosθ)
= 2r^2 (1-cos(S/r))
indigo trout
yea, that answers my question. i was more so looking to see where my logic was flawed coz it seemed at little fish that i did not encounter any trig
its not a hard google search lol thank you so much
appreciate you taking the time to help
.close
safe radishBOT
winter pivot
Ok your mistake as I said is in your treatment of the vector u.
In Cartesian coords:
u = <r(1-cosθ), -rsinθ>
safe radishBOT
Available help channel!
lunar halo
hello, I am not sure if my work is sufficient to prove the series converges.
lunar halo
sorry
it converges by geometric series because r<1 but I'm not sure if I need to prove anything further that n^2 doesnt outspeed r
or if the fact that it is alternating plays a part
safe radishBOT
@lunar halo Has your question been resolved?
light shoal
the fact that is alternating doesn't have any impact (the series converges absolutely), but of course you need to show that n^2 doesn't affect convergence
safe radishBOT
safe radishBOT
Available help channel!
lean otter
Say two functions f: A -> B and I_B: B -> B
Composition of functions is allowed if B is a proper subset of B here, or if the range(f) is a proper subset of B.
But here, this isn't the case. B is an improper subset of B.
Then why is f o I_B = f valid?
I know how to prove this, thanks to Cogwheels of mind's help, but I pondered across this issue after that and I'm stuck.
safe radishBOT
Say two functions f: A -> B and I_B: B -> B
Composition of functions is allowed ...
@lean otter Has your question been resolved?
lean otter
<@&286206848099549185>
lean otter
Say two functions f: A -> B and I_B: B -> B
Composition of functions is allowed ...
Source from where I studied:
peak estuary
but $f\circ I_B = f$ is not valid
flat frigateBOT
Denascite
peak estuary
the right hand side takes an input from A and gives an output from B
the left hand side takes an input b from B, then I_B gives the same output b back and then you try to put it into f
but f(b) is not defined
on the other hand $I_B \circ f = f$ is valid. $(I_B \circ f) (a)=I_B(f(a))=f(a)$
flat frigateBOT
Denascite
peak estuary
some textbooks sadly defined the order of composition to be the other way around
so $g\circ f = f(g(x))$. but that's disgusting
flat frigateBOT
Denascite
lean otter
on the other hand $I_B \circ f = f$ is valid. $(I_B \circ f) (a)=I_B(f(a))=f(a)$
Okay I_B o f = f but, because of f: A -> B and I_B: B -> B, then by definition I_B o f will be composite if B is a proper subset of B which is not true, see the screenshot I sent earlier here)
safe radishBOT
Okay I_B o f = f but, because of f: A -> B and I_B: B -> B, then by definition I...
lean otter
Source from where I studied:
This one
peak estuary
are you sure that textbook doesn't just use $\subset$ to also mean $\subseteq$ ?
flat frigateBOT
Denascite
peak estuary
I don't like that notation either but it's something people use
lean otter
are you sure that textbook doesn't just use $\subset$ to also mean $\subseteq$ ?
I think, because by the proper subset notion, nothing makes sense, like in this problem
Oh I see so it's the conventional use of denoting improper subset here
Thank you o7
.close
valid vortex
Can someone answer and explain this
safe radishBOT
Can someone answer and explain this
maiden mural
from what i understand , its asking for the area of the triangle + area of that square. am i right?
valid vortex
yea
safe radishBOT
@valid vortex Has your question been resolved?
safe radishBOT
@valid vortex Has your question been resolved?
frigid beacon
so are you asking how to find the areas of triangles and squares?
regal girder
the area of a rectangle is a * b, the area of a right triangle comes from that basically
if you need the formulas that is
for a square, it's just a rectangle where a = b
safe radishBOT
@valid vortex Has your question been resolved?
fierce basin
Can someone answer and explain this
Area of triangle+ area of square
40×40 + (300×40)÷2
safe radishBOT
@valid vortex Has your question been resolved?
wary wigeon
safe radishBOT
wary wigeon
can I ask clarification for this question?
vocal portal
1 standard deviation in normal distribution is about 67% as I recall
it's denoted by sigma
the 3 sigma rule was almost everything (99.3%) is contained within it
it's all about calculating field over distribution
use some online calculators
wary wigeon
What is needed for letter B question is it the answer if I get P[-a<Z<a] or I should get the value for Z?
vocal portal
P(Z) and draw Z
wary wigeon
I already have values here, I'm just confused what is the final answer for question in B
vocal portal
it was: find probability
wary wigeon
Yep, so it is the answer if solve this
P[-0.5<Z<2.25]
Right?
vocal portal
and why would you want to plug juat ratio?
unless you have some other working function
but that can work
though it's not mathematical notation I think
wary wigeon
So what value will I put as a final answer for question in B?
I have two values here
wary wigeon
Let's compare what we got
wary wigeon
Isn't that sigma² is 16?
vocal portal
it is
vocal portal
this plot is also half your answer
you may copy it
right sigma squared is 16
that's the waay it takes it as an input
you are correct
wary wigeon
thanks
safe radishBOT
@wary wigeon Has your question been resolved?
wary wigeon
In that problem, in letter C, after I solve for z score, do i need to subtract it to 1 so that I will get the percent of the bags that passed?
safe radishBOT
@wary wigeon Has your question been resolved?
wary wigeon
vocal portal
for previous C it will be juat less than 350
wary wigeon
for previous C it will be juat less than 350
wary wigeon
@vocal portal is this what you mean?
wary wigeon
so over 350
yes
wary wigeon
for previous C it will be juat less than 350
@vocal portal can you help me with this?
vocal portal
you can rebuild function in wa to get the answer
wary wigeon
i have my answers here for Z and X but i don't know if it is right.
vocal portal
because seeked variable will be under integration
should be
if you plugged it correctly
for laat question try plugging:
N(65,3.5^2) from 65-x to 65+x is equall to 0.68
or
integrate 65-×..65+× N(65,3.5^2) dx = 0.68
sorry I go to sleep
wary wigeon
thanks
marsh walrus
its not -2
remember z scores move by standard deviation
if you move one standard deviation away from the mean, your new z score is 1
from here you should use any ol z table
whats the total of the z table up to -1
is the problem asking for this, or its complement
wary wigeon
so my z-score for this item is wrong?
marsh walrus
it is not -2
try drawing a picture
alternatively you seem to wanna understand this stuff or whatever but
heres the answr
you should be able to work backwards from this
but Z is not -2
the defining characteristic of the standard normal distribution is that if you move like that=
like if you move 1 standard deviation from the mean, you are now at 1
wary wigeon
i'm not submitting it yet
marsh walrus
why not?
marsh walrus
68% is one of your standard values
there should be no calculation
how much if a normal distribution is between the mean, plus or minus one standard deviation
wary wigeon
i used the empirical rule but my professor wants z and X
marsh walrus
sure
can you use the empirical rule to get it?
because you can cite i mean
what is the z score of 68-3.5
once you transform this thing to standard normal
marsh walrus
the defining characteristic of the standard normal distribution is that if you m...
.
but your z value sounds not right
idk what they want you to put there, since ther should be two
wary wigeon
i got the age range of 61.5 to 68.5
marsh walrus
that sounds good
idk how precise your teacher wants you to be
since obviously its not gonna be exactly that
since plus or minus one std dev isnt exactly 68
but then why are they saying 68
seems like you should use empirical rule to calculate everything here
wary wigeon
i still need to check this
Is this problem can't be solved using the normal calculation?
marsh walrus
sure you could
you split it up
you wanna move 34 in each direction
so your values are score is $\frac{65 \pm x }{ 3.5 } = \pm \Phi ^{-1} \qty( \frac{1-0.68}{2} )$
err
flat frigateBOT
jan Niku (LinAlg Study Group)
flat frigateBOT
Result:
0.16
so we go up to 0.16 on the left
away from .84 on the right
in between we have
,calc 0.84-.16
flat frigateBOT
Result:
0.68
What is the z score then?
marsh walrus
never figured out how to get calc to do it
one sec
well
try using your table
look for 0.16
wary wigeon
A moments
marsh walrus
sure
wary wigeon
A moment*
marsh walrus
heres where i find it
but you might have a nicer table
In our class we interpolated/averaged, so I'd get ||plus or minus 0.995|| i think? but you should try yourself
flat frigateBOT
jan Niku (LinAlg Study Group)
wary wigeon
I got 61.52
marsh walrus
yea so like
wary wigeon
So i will round this up right?
marsh walrus
really really close
wary wigeon
For age?
marsh walrus
i dont think round up
age is continuous
at least i think so
you can be 38.732 years old
wary wigeon
Thanks
jovial yew
can anyoe know this?
wary wigeon
So my z is -0.99 and my x is 61.52
marsh walrus
you have two z's
and two x's
but since its symmetric there is no more calculation to do
marsh walrus
👀 you have to trust yourself at some point lol
wary wigeon
marsh walrus
well my advice would be use a calculator
find a calculator to check since itll be faster and youll learn
safe radishBOT
@wary wigeon Has your question been resolved?
frank vine
safe radishBOT
frank vine
For a) I've got 14/55
native eagle
For a) I've got 14/55
Yes you’re right
native eagle
How would I do b and c?
(b) is similar to (a). Think of the expression in (a) to be $\dfrac{C^9_4 C^3_0}{C^{9+3}_{4+0}}$ (i.e., choosing 4 good units from 9 of them, and choosing 0 bad units from 3 of them).
flat frigateBOT
pi over four
frank vine
(b) is similar to (a). Think of the expression in (a) to be $\dfrac{C^9_4 C^3_0}...
w h a t
Ohh
I don't really understand tbh
native eagle
In the scenario in problem (b), you are choosing 2 good units and 2 bad units
So the numerator should be changed so that it represents the number of ways to do so
frank vine
I was thinking it was either 9/12*8/11*3/10*2/9
frank vine
So the numerator should be changed so that it represents the number of ways to d...
The numerator of what exactly
native eagle
(b) is similar to (a). Think of the expression in (a) to be $\dfrac{C^9_4 C^3_0}...
The numerator of this
frank vine
?
native eagle
I was thinking it was either 9/12*8/11\*3/10\*2/9
There are 6 ways to rearrange the order though. Suppose G represents a good unit and B represents a defective unit, choosing it in the order of GGBB is different from choosing it in the order of GBGB. Therefore, considering all permutations of 2 good units and 2 defective units, you should multiply this by 6.
frank vine
There are 6 ways to rearrange the order though. Suppose G represents a good unit...
Would order matter in this case?
It would be combinations and not permutations right?
native eagle
Would order matter in this case?
Yes it does, if the denominator is 12*11*10*9
native eagle
It would be combinations and not permutations right?
If you do it the way I did, then it would be combinations.
frank vine
Yes it does, if the denominator is `12*11*10*9`
Huh
native eagle
I was thinking it was either 9/12*8/11\*3/10\*2/9
This one is considering permutations, but it also works
frank vine
Wait so is the answer 9/275
native eagle
Wait so is the answer 9/275
No, it’s not the answer
native eagle
Yeah
frank vine
And the second would be 8/11?
native eagle
And the second would be 8/11?
Yeah
frank vine
so if there are 2 proper pieces now we have to find the defective ones correct
so would it be 3/10 and 2/9?
native eagle
so if there are 2 proper pieces now we have to find the defective ones correct
But the first one and the second one could be defective too, if the third one and the fourth one are good
frank vine
oh
native eagle
So you need to consider the case when the good ones are:
• 1st and 2nd
• 1st and 3rd
• 1st and 4th
• 2nd and 3rd
• 2nd and 4th
• 3rd and 4th
And then add them up
frank vine
confusion
native eagle
But actually each case has the same probability
frank vine
each case has a 2/12 probability?
native eagle
each case has a 2/12 probability?
No, same probability given that there are 2 good units and 2 defective units. It is conditional.
native eagle
So you need to consider the case when the good ones are:
• 1st and 2nd
• 1st an...
i.e., the probability of each case is (1/6) Prob(2 good and 2 defective)
Simply put, the probabilities of these 6 cases do not add up to 1, they add up to the answer of (b).
native eagle
Yep im lost beyond all hope
I’m quite terrible at explaining, sorry 🥲
Actually practising to explain math to people
native eagle
wait order would matter for this right
Yes
frank vine
I’m quite terrible at explaining, sorry 🥲
Actually practising to explain math t...
Oh that's alr
could you like write ur work down or smthn and send it to me
i dont need the answer
i just need to figure out how to do this
native eagle
I will do (b) as an example and leave a hint for (c)
Here, order does not matter because the order does not matter for 12C4.
frank vine
THAT MAKES SO MUCH SENSE
native eagle
If I replace it by 12P4, then order would matter in the numerator
native eagle
So when do I use P and when do I use C
When you are calculating probability, I would suggest you to stick with C, and see nPr as nCr • r! (choosing r objects from n of them and rearranging).
frank vine
would c be (9C2*9C3*9C4)/12C4?
frank vine
When you are calculating probability, I would suggest you to stick with C, and s...
Ohh
native eagle
No, it would be P(2 good, 2 defective) + P(3 good, 1 defective) + P(4 good)
frank vine
h u h
native eagle
Each of the calculations is similar to the one I did here
native eagle
h u h
Oh, P() means the probability of an event here
Should have written it as Prob()
frank vine
Oh, P() means the probability of an event here
Yeah I know what P is but
Why did you use P
oh wait
woudl you multiply
native eagle
Since we are dividing the scenario “at least 2 good” into the sub-cases “2 good”, “3 good”, and “4 good”, we are actually adding the 3 probabilities. They are different cases.
native eagle
Or would you add that
You add that
native eagle
cause that would be 54/55
Yes
Because it is quite hard to choose all 3 defective units if you are just choosing 4, so it makes sense
You would be quite “lucky” to choose 4 things from 12 of them and got all 3 defective ones
native eagle
I’m glad my explanation helped 😉
native eagle
Yes, that is right
native eagle
Think of an event with 1/10 probability, perhaps a lucky draw with a 1/10 chance of getting the best prize. It would be quite unusual to get the best prize 3 in a row, right?
That’s why the probability is so small
native eagle
It should be (-1)^101 rather. Since the expression the 101-th power of a binomial, it is not possible to have a term with ^102 power.
native eagle
The first term would be x^101(x)^0 right
x^101 (-1)^0 rather
native eagle
Yeah that's what I did too
frank vine
Wait it would become 6! right
native eagle
Wait it would become 6! right
No, if you evaluate 2! and 3! one by one, you get (2!)(3!) = (2)(6) = 12, and 6! = 720
frank vine
Oh I'm stupid
native eagle
Oh I'm stupid
Nah, everyone makes mistakes
frank vine
mods if you see this just know the this person is an amazing teacher
10/10 would ask for help again
@native eagle for the first one it would be 14/55 right
not 9/275?
native eagle
<@297921140565868544> for the first one it would be 14/55 right
Yeah
safe radishBOT
safe radishBOT
Available help channel!
safe radishBOT
spark gazelle
Not sure what I'm doing wrong; kinda lost thankss
safe radishBOT
Not sure what I'm doing wrong; kinda lost thankss
spark gazelle
my teacher gave me this but not sure what to make of it; its not the same as the actual question its just a sample
lean otter
Ok so you got the time to complete 5 revs. Divide the time by the 5 revs to get the time for 1 rev.
$$ T = \frac{60+16}{5} = 15.2 ,\mathrm{s/rev}$$
Now divide a whole revolution by the time to get the ω.
$$ \omega = \frac{2\pi}{15.2} = 0.413 \mathrm{rad/s}
flat frigateBOT
Ausaramun
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
lean otter
Convert the omega from rads to degrees.
$$ 0.413(\frac{180}{\pi}) = 23.684 , \mathrm{degrees/s}$$
flat frigateBOT
Ausaramun
safe radishBOT
@spark gazelle Has your question been resolved?
lean otter
Now remember the straight line equation? We'll use that for getting the angle exactly.
Instead of y, we will put θ. And instead of the slope, we will put ω and instead of the y-intercept, we will put the initial angle.
$$ \theta = \omega t + 45°$$
flat frigateBOT
Ausaramun
spark gazelle
ohhhh
lean otter
We want the angle when the time is at 255 seconds exactly. We replace t with 255 and we get the angle.
Now when you get the angle, it will be a big number. It is exactly 6084.4736...°.
spark gazelle
yeyeye thats what i got
lean otter
What we do is divide it by 360, which will give 16.9. Take the 16 only, multiply it by 360 and minus it from the number you got originally, which is 6084.4736
Wait
We forgot the counterclockwise direction consideration
spark gazelle
wait could you just subtract it and get 324.4736 and convert it to rad and we get 5.66
spark gazelle
wahhh thank u then how would we find the coordinates
lean otter
Coordinates, they gave you the coordinates of the initial position.
You get the radius using Pythagorean.
It will give you $\sqrt{2}$
flat frigateBOT
Ausaramun
lean otter
We got the radius and the angle. All we do multiply the radius with sine of the angle and cosine of the angle.
The cosine is the x coordinate and the sin is the y coordinate
spark gazelle
.close
sharp sage
$$\frac{d}{dx}\log\left(\log\left(x\right)^{\log\left(x\right)}\right)$$
flat frigateBOT
Chunkin
sharp sage
how do you solve this goofy problem
grave swallow
Chain rule a bunch of times maybe
Or implicit differentiation idk
Wait
Just product rule + chain rule
No
You can bring power to the front
Lmao
It’s inside of a log
shadow glade
Yeah itll just be log (log^2 x) = 2log(log(x)) then chain rule
unique bison
Chen lu
shadow glade
log(x)*(log(log(x))
This is wrong…
unique bison
I heard they have a cousin called quo shun lu
safe radishBOT
@sharp sage Has your question been resolved?
safe radishBOT
safe radishBOT
Available help channel!
safe radishBOT
fossil shell
wouldn’t it be 1.091^2
unless I’m misunderstanding the question
what does “effective rate of interest” mean
yeah but how often is it
modern storm
compounded semi annually means twice a year
fossil shell
can you phrase the first sentence in easier to understand terms
like what is it saying
safe radishBOT
@modern storm Has your question been resolved?
fiery valley
what they mean with "unique"?
fiery valley
.close
remote flint
safe radishBOT
remote flint
how exactly would i solve this problem?
nova creek
What have you tried?
safe radishBOT
@remote flint Has your question been resolved?
remote flint
i just don’t know how to solve the problem
nova creek
Well, you can find the length of the bottom solid line. After that, if you can find the angles of the big triangle, you can use the law of sines. That's a possible method
remote flint
thank you
clever dune
Two investments are made at the same time. The first consists of investing 1670 dollars at an annual rate of interest of 10.6 percent, compounded semiannually.
The second consists of investing 1550 dollars at an annual rate of interest of 10.6 percent, compounded daily.
How long will it take for the two investments to be worth exactly the same amount in years?
can anyone help with this?
safe radishBOT
Two investments are made at the same time. The first consists of investing 1670 ...
fossil shell
what have you tried so far?
fossil shell
what are you solving for?
clever dune
what are you solving for?
n, (time) in years
clever dune
by setting both investments equal to each other with their respective compounding effective rates and solve for the n value
fossil shell
by setting both investments equal to each other with their respective compounding effective rates and solve for the n value
how would you do the solving part, specifically?
clever dune
> by setting both investments equal to each other with their respective compound...
for 1670, its compounded semi annually so, (1 + 0.07 /2) ^2 = 1.071225, and for 1550, its compounded daily so (1 + 0.07 / 365) ^ 365 = 1.07250
clever dune
you could apply exponent rules
fossil shell
is there a way to get n out of the exponent?
clever dune
ln(1670) + nln(1.071225) = ln(1550) + nln(1.07250)
safe radishBOT
@clever dune Has your question been resolved?
fossil shell
np
junior wagon
safe radishBOT