What does he mean by pointing u to poly and t(u) to vector
#help-0
limpid lotus
shrewd olive
<@&286206848099549185>
lone heartBOT
@shrewd olive Has your question been resolved?
shrewd olive
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rotund crater
help
rotund crater
is 1/4?
last ether
Yes
last ether
Well it's just the length of the interval divided by how many parts you want
rotund crater
Well it's just the length of the interval divided by how many parts you want
soo my procces is correct?
last ether
Yeah
normal jasper
i can code this but i have no idea what its even asking of me, when i send back a polynomial, how do i determine the coefficients, i simply don't understand the question
tacit arch
i can code this but i have no idea what its even asking of me, when i send back ...
read the powers of x and y separately on each term
$xy = x^1 y^1$
ocean sealBOT
riemann
normal jasper
i don't understand your point
im just confused on why a(4,2) is =2 and why the others not stated are 0, it can't be arbitrary...
tacit arch
im just confused on why a(4,2) is =2 and why the others not stated are 0, it can...
what's the coefficient of this term?
tacit arch
read the powers of x and y separately on each term
and then identify the powers of x and y on that term
normal jasper
yea i can see that, but when im creating the program i dont get how im supposed to determine the coefficients
tacit arch
i can code this but i have no idea what its even asking of me, when i send back ...
you said you can code this?
if you understand the math but don't understand how to code it, i suggest CS server in #old-network
tacit arch
what's the coefficient of this term?
.
normal jasper
2..
tacit arch
yea i can see that, but when im creating the program i dont get how im supposed ...
you said you can see it
tacit arch
and then identify the powers of x and y on that term
now answer this one
normal jasper
4 and 2
normal jasper
yes i know but in a general case when im considering n degree, how are they computing that a(4,2) = 2 and determining that the rest are 0, it can't just be arbitrary right?
tacit arch
yes i know but in a general case when im considering n degree, how are they comp...
there are two degrees to track
i, j
tacit arch
yes i know but in a general case when im considering n degree, how are they comp...
i just explained it
you "read off the coefficients"
normal jasper
its the coefficient because its' the coefficient?
tacit arch
yes when the same word is used in different places, they refer to the same thing
normal jasper
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humble tinsel
Country Day's scholarship fund receives a gift of $ 180000. The money is invested in stocks, bonds, and CDs. CDs pay 3 % interest, bonds pay 3.8 % interest, and stocks pay 6.8 % interest. Country day invests $ 40000 more in bonds than in CDs. If the annual income from the investments is $ 8320 , how much was invested in each?
lone heartBOT
Country Day's scholarship fund receives a gift of $ 180000. The money is investe...
pale scroll
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waxen flame
What have you tried?
lone heartBOT
@pale scroll Has your question been resolved?
pale scroll
Stuck there
waxen flame
Recall that you are calculating a semicircle. What is the area for a semicircle?
pale scroll
1/2(pi r^2)
waxen flame
So how should you change the integral?
Let's try to understand what the question is asking you.
lone heartBOT
pale scroll
i have another questio
waxen flame
.reopen
lone heartBOT
✅
waxen flame
What's your question?
waxen flame
No.
slender quiver
!show
lone heartBOT
Show your work, and if possible, explain where you are stuck.
waxen flame
How did you get that answer?
waxen flame
Do you understand how integrals work?
pale scroll
the derivative of sin is cos, but after that, im stuck
waxen flame
Do you understand how integrals work?
waxen flame
I mispoke.
The change in a function between the points a and b, where b is greater than a, can be calculated using this expression, f(b) - f(a).
Does that make sense?
pale scroll
yes
waxen flame
To use an example, no matter how to get between those two points, the change in f(b) - f(a) will always be the same.
No matter how we change that curve, move it up or move it down, if it starts at point A and ends at point B, Δy will always have the same value.
This is a major premise behind integrals. If we add all the little changes that occur between points A and point B will always result in the function ending at point B.
The function of that graph is the antiderivative of f(x) = -x*(x-4).
The sum of every value on the blue line, ie. the area, represents the total change that occurs in the black line.
This gives us the equation
$\int_{a}^{b} f(x) dx = F(b) - F(a)$
ocean sealBOT
Kookiemon
pale scroll
yes
waxen flame
Now, the question is asking about the derivative of an integral.
Which in effect is the derivative of F(b) - F(a).
Which we know is f(x).
pale scroll
this problem is a a volumes of solid of revolution?
waxen flame
Yes, but not a full revolution, only a half revolution because it asked about a semicircle.
The base of the semicircle is given as a slice of the region R that is perpendicular to the x-axis.
The base of the semicircle is represented by the black line segment and is the diameter of the semicircle. You have to imagine the semicircle projecting out away from the screen.
pale scroll
so I should use (pi r^2)/2 dy?
waxen flame
Yes, and you would have to account for the radius as well.
You are given a diameter as 2x - x^2, however the radius is half of that.
pale scroll
should I solve 2x-x^2 and then divide the result by two?
waxen flame
Yes, that will give you the radius, r.
waxen flame
This will give you a full revolution.
But you only want half of that.
This will help you visualize what you are trying to calculate.
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wind canyon
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wind canyon
Hello can someone help me with question 2(b)
royal depot
alright so first of all
think about which values would fit into that statement
|x|+3x>1
for example, |(2)|+3(2)>1 because 2+3*2=2+6=8 so that point would be shaded
and 8>1
a hint is to find the value equal to |x|+3x>1
@wind canyon
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@wind canyon Has your question been resolved?
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halcyon monolith
**[Matrices and Eigenvectors] Having difficulty getting an Eigenvector for the matrix [1, 1; -1 1]
**
Here's what I have done so far
When I have tried to solve for eigenvectors, no matter which component of the Eigenvector I kept as constant, the eigenvalue would have been the same, but for the second eigenvalue [1-i] of the vector [1, 1; -1 1], this isn't true.
If I choose x_2 as constant, I would get Eigenvector to be X = [1; i]
But, if I choose x_1 to be constant, I would get the Eigenvector to be X = [1; -i]
My professor told me, that this won't happen (not for this particular problem but generally)
So my questions
- Which Eigenvector should I choose and why?
- Why are the Eigenvectors different?
I ran a python program on this and I got this result But, obviously, that doesn't solve my problem.
Much Thankful for your help
lone heartBOT
@halcyon monolith Has your question been resolved?
halcyon monolith
<@&286206848099549185>
gleaming ridge
- You don't need to choose any of them
Because they are both false
Your second eigenvector must be X2 = [i ; 1] k
And the right answer is of course "d" !
halcyon monolith
Your second eigenvector must be X2 = [i ; 1] k
I believe you are saying that for the eigenvalue 1-i
But, I don't understand how it is wrong.
what's wrong?
Please explain if possible.
gleaming ridge
I didn't understand it either xD
But if I were you, I wouldn't even bother to compute the second eigenvector!
It has been proved that if L1 and L2 are the eigenvalues of a 2x2 marix, and that they are complex conjugates
Then their respective eigenvectors must also be complex conjugates
You computed X1 without any problems, that is good
Then just obtain X2 as: X2 = X1*= [i ; 1] k
halcyon monolith
Then their respective eigenvectors must also be complex conjugates
I didn't know this. Damn... but thank you tho! you helped
.close
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atomic jewel
If t is in quadrant II and sint=1/6, what is cos2t?
I got 10/12 and just wanted to make sure if I got the right answer
tacit arch
,tex .double angle
ocean sealBOT
riemann
tacit arch
Did you use one of those first 3
atomic jewel
I used the cos(2) formula
gray isle
show work
atomic jewel
kk
tacit arch
cosine is negative in the second quadrant so that part's wrong at least
gray isle
cos(t) is neg, doesn't mean cos(2t) is neg
atomic jewel
gray isle
(1/6)^2 isn't 1/12
atomic jewel
it isnt?
gray isle
what makes you think it is
vale wigeon
(1/6)^2 is not 36
vale wigeon
it may be what you meant but it wasn't what you said.
gray isle
result can be simplified
atomic jewel
result can be simplified
by 2?
gray isle
what by 2
vale wigeon
⚠️ but yes, 34/36 = 17/18
atomic jewel
ah ok
and I also had a question about this other problem
"If t is in quadrant III and cost = - 1/5, what is sin(t/2)?"
atomic jewel
**riemann**
would I use the 2nd formula for this?
gray isle
no,
recognise that the question is flawed an raise the issue with whoever gave it to you
gray isle
is cos positive or negative in Q3?
atomic jewel
negative since quadrant 3 is the bottom left square
OH
I'm so sorry I forgot to add the negative
ty for pointing that out
livid patrol
do i need to like open a ticket or something for help or do i just send stuff i need help witth?
tacit arch
do i need to like open a ticket or something for help or do i just send stuff i ...
!help
lone heartBOT
do i need to like open a ticket or something for help or do i just send stuff i ...
Please read #❓how-to-get-help
atomic jewel
there are half angle identities
is this to me? or galactic?
gray isle
you
tacit arch
,tex .half angle
ocean sealBOT
riemann
gray isle
NEVER use 0 as a substitute for theta
atomic jewel
Idk how else to put theta onto keyboard
so I just used it to substitute theta in the text
atomic jewel
ah ok
so would I use Sin(t/2) to solve this equation?
or
would I got about it with a different formula?
@gray isle
lone heartBOT
@atomic jewel Has your question been resolved?
gray isle
you're interested in sin(t/2)
and are given cos(t)
so you use the one that has those
atomic jewel
ah ok
atomic jewel
you're interested in sin(t/2)
and are given cos(t)
so you use the one that has t...
I'm assuming this is wrong?
atomic jewel
-1/5 isn't 1/5
wdym?
gray isle
how are you doing this
sure 1 = 5/5
but why did (-1/5) get changed to 1/5
and also the sqrt should be clearly over the whole fraction, not just the numerator
atomic jewel
but why did (-1/5) get changed to 1/5
I assumed that the - outside of -(-1/5) would
turn it positive
atomic jewel
oh damn you're right
gray isle
as for second issue
and also the sqrt should be clearly over the whole fraction, not just the numerator
and then choose the appropriate sign based on the location of t/2
atomic jewel
as for second issue
> and also the sqrt should be clearly over the whole fractio...
so I should add a ^2
over the whole thing?
atomic jewel
you said sqrt?
gray isle
^2 is indicating the raising to the power of 2 (squaring, is not the same as square rooting)
as indicated in the identity, the radical covers the whole fraction
square root
gray isle
they way you're writing still isn't clear enough
ideally you'd also have () when you have skyscraper fractions
atomic jewel
they way you're writing still isn't clear enough
what else should I include?
gray isle
you should pretty much be able to form a box enclosing the radicand if you were to draw those vertical/horizontal red lines
as for the issue with skyscraper fractions, use parentheses as I've done.
it isn't necessary if the lengths are distinct enough by makes it easier to read regardless
gray isle
gray isle
and so would I divide 6/5 by 2?
for that part, yes
gray isle
use () to clearly indicate what's being rooted
similar notation issue to the above
sqrt(3/5)
and then choose the appropriate sign based on the location of t/2
atomic jewel
atomic jewel
use () to clearly indicate what's being rooted
like this?
oh wait would I put 3/5 in ()?
gray isle
if you're communicating in plain text
writing properly on paper above like that, parentheses aren't needed
atomic jewel
oh pog
atomic jewel
writing properly on paper above like that, parentheses aren't needed
so this is the answer?
gray isle
and then choose the appropriate sign based on the location of t/2
did you do the work related to that?
to see whether you should have sqrt(3/5) or -sqrt(3/5)
atomic jewel
> and then choose the appropriate sign based on the location of t/2
did you do t...
I didnt know the sqrt could be negative
How would I go about that?
atomic jewel
consider what interval theta is in
what does that mean?
gray isle
you are told theta is in Q3 right?
atomic jewel
you are told theta is in Q3 right?
yep
gray isle
what angles are in that quadrant
atomic jewel
what angles are in that quadrant
180 to 270
atomic jewel
180° < theta < 270°
what does that tell you about theta/2
it's greater than 180 but less than 270
gray isle
no
don't overthink what i'm asking
$180\deg < \theta < 270\deg
\implies ? < \frac{\theta}{2} < ?$
ocean sealBOT
ℝamonov
atomic jewel
Im so lost
vale wigeon
would you like to be asked the same question but in different words?
atomic jewel
yeah I think that would help
vale wigeon
Mary says, "I have somewhere between $180 and $270 in my wallet."
John says, "I have exactly half as much money as Mary does."
what can you say about the contents of John's wallet?
atomic jewel
john has half the money mary does
vale wigeon
... that is just restating the problem
so not really what i was looking for here...
john has between ___ and ___ dollars
can you fill the blanks here
atomic jewel
john has between 90 and 135 dollars
vale wigeon
ok
so you do understand this basic algebra
$180\dg < \theta < 270\dg \implies 90\dg < \theta/2 < 135\dg$
ocean sealBOT
Ann
vale wigeon
does this make sense to you now
atomic jewel
yep!
looks like I learned another thing today
can I try the same problem but switch up the numbers to see if I got it?
vale wigeon
uh yeah sure but tell us the problem w/ the switched-up numbers so we are on the same page
vale wigeon
k
atomic jewel
IM SORRY 😭
oh wait
wrong problem
"If t is in quadrant III and cost = - 1/8, what is sin(t/2)?"
meant to switch this up
I got sqrt(3/8)
atomic jewel
sqrt(3/8) looks incorrect to me.
Ye I accidentally did a massive miscalculation
this is my 2nd attempt
vale wigeon
your work is once again poorly written
ramonov already pointed out the issues with how you write your radical symbols
they're just hanging there like something hastily slapped on
atomic jewel
they're just hanging there like something hastily slapped on
I'm sorry 😭
I'll make them better
is this better?
vale wigeon
not really
atomic jewel
MAN
ocean sealBOT
Ann
vale wigeon
from a typesetting perspective
vale wigeon
sqrt((9/8)/2) is correct but what did you do afterward?
any mistakes you make from this point on are arithmetical and NOT trigonometric in nature
atomic jewel
sqrt((9/8)/2) is correct but what did you do afterward?
I thought I was supposed to divide by 2
vale wigeon
??
do you have any written work to show for how you did the calculation
or did you try to do it all in your head
atomic jewel
or did you try to do it all in your head
I tried doing it in my head the 1st attempt
vale wigeon
don't.
vale wigeon
...
communication breakdown!
okay, let me try again.
you say that your final answer is sqrt(3/8). is that or is that not the case?
atomic jewel
No
vale wigeon
okay then what answer did you get?
atomic jewel
the second attempt I'm currently at 9/8 / 2
atomic jewel
sqrt(9/8) / 2
atomic jewel
how would I simplify that?
vale wigeon
well
simplify the fraction inside the root first
do you know how to divide fractions in general?
atomic jewel
not a fraction like this
vale wigeon
what if it was (9/8)/(2/1) instead?
atomic jewel
9/16
atomic jewel
would it just be 9/16 ?
vale wigeon
no
the square root of a number, with exactly two exceptions, is not equal to the number itself!
sqrt(9/16) = sqrt(9)/sqrt(16) = 3/4...
vale wigeon
this was self-studying you were doing, right?
vale wigeon
yeah okay so
you need to self study basic arithmetic and algebra
fractions
roots
all that shit
right now you are struggling with them way too much to be doing trig
atomic jewel
you need to self study basic arithmetic and algebra
yeah that seems like a good start!
ty for the help!
I also think I started struggling because i've been studying all day and it's currently 3am for me
I'm usually a lot better at this stuff
but I'm just exhausted rn
that being said
@vale wigeon ty for the help today!
really appreciate it
when I'm well rested, I'll go over some stuff I learned here
atomic jewel
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lone heartBOT
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wraith flint
not sure how this linear transformation would work
lone heartBOT
not sure how this linear transformation would work
wraith flint
i think b is an element of r^3
given the transformation matrix is the indentity matrix the linear transformation should be going from R^3 to R^3
but T being an element of R^4 just confuses me
lone heartBOT
@wraith flint Has your question been resolved?
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@wraith flint Has your question been resolved?
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twin estuary
surreal nest
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golden canyon
@surreal nest you changed your exponent
golden canyon
should make it a bit smaller
surreal nest
Which one smaller
golden canyon
surreal nest
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silent plume
how do I go about finding m and b?
lone heartBOT
how do I go about finding m and b?
silent plume
m and b being the last two boxes respectively
gray isle
think about what you can do with the derivative you just found
silent plume
hmmmm
I can substitute x or y from the coordinates into the equation
the derivative is the slope of the curve, no?
I tried substituting x in y' with 0.0016 but it says that was wrong
gray isle
why are you subbing x with 0.0016
silent plume
sorry I meant 2
gray isle
show the work you're doing
silent plume
-10 / (5(2) +15)^3 = -0.00064
oh I forgot to input the negative in the answer
to find b I'll do 0.0016 = -0.00064(2) + b
- -0.00064(2)
b = 0.00288
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tame pike
When performing proofs, what is more appropriate?
Q.E.D. or triple dots?
alpine sable
I am a $\qedsymbol{}$ person
ocean sealBOT
Toby
lone heartBOT
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pale scroll
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pale scroll
can someone help me with this one
alpine sable
think about what 'at rest' means
pale scroll
0
alpine sable
what is 0?
pale scroll
a(t)=0, its correct?
alpine sable
a means acceleration?
0 acceleration means constant velocity
recall that velocity is the derivative of displacement, and acceleration is the derivative of velocity
pale scroll
so it would be v(t)=0
alpine sable
yes
restive chasm
I think the answer could be either v (t) = 0 for complete rest and v(t) changes sign for momentarily rest. So both correct.
lone heartBOT
@pale scroll Has your question been resolved?
alpine sable
I've got this one question in math. It's really simple, I've just been not listening to classes so I don't really know how to solve it.
Basically, it goes something like this:
There is a right angled triangle ABC with these lengths: 9cm, 12cm and 15cm.
A. What is the area of this triangle?
I answered this one easily, I just did 12cm x 9cm and divide that by 2, and it came out to be 54cm.
B. Find the "other height". I've got no idea what an "other height" is, and I don't know how to calculate it. Someone help
stray night
I've got this one question in math. It's really simple, I've just been not liste...
the purple line?
alpine sable
yea i think thats the other height or wtver its called
no idea how to solve it
@stray night
use the area formula and rearrange for height
alpine sable
use the area formula and rearrange for height
how do i do that
use base = AB
so AB is 15
and uhh
idk bro im dumb asf
@alpine sable
alpine sable
the purple line?
look at this diagram
purple is your height, AB is 15
you've found the area in part A
ornate leaf
the triangle formula =
base * area / 2 = area
the purple line is the height you want, and the corresponding base is c, so you can just subsitute it back in
lone heartBOT
@alpine sable Has your question been resolved?
lone heartBOT
@alpine sable Has your question been resolved?
stray night
can anyone help
lone heartBOT
can anyone help
stray night
i don't even know how the picture looks like
stray night
ornate leaf
ok i dont really know how to do but heres the picture
with a really weird DNF circle
quasi vector
!nosols
lone heartBOT
As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.
ornate leaf
?
ornate leaf
(no idea)
stray night
stray night
well 13.7X
what
ornate leaf
decimal
so if i round to nearest integer im 14
whats up guys im 14 and this is deep
stark path
ornate leaf
we're the same age
🤝
quasi vector
put in all the details that you know about the question
ornate leaf
whats up bbg
stray night
put in all the details that you know about the question
then what
stray night
whats up bbg
stray night
send me your figure
ignore the upper part
lone heartBOT
@stray night Has your question been resolved?
stray night
<@&286206848099549185>
stray night
Lemme grab a pen and copy real quick <@1011533999283384340>
okayyy
frigid swallow
The question has a figure?
stray night
The question has a figure?
what?
lone heartBOT
@stray night Has your question been resolved?
stray night
.close
pale kestrel
There's splitting into cases/brute force but could there be a nicer way to calculate:
A 52 playing card deck has 37 cards left. There are 2 Aces in these 37 cards.
Amongst these 37 cards and 8 other cards not in the deck (= 45), there are 2 9's.
We draw 2 cards from these remaining 37 cards. What is the probability at least one Ace or 9 is drawn?
pale kestrel
Looking for suggestions for approaches you'd take - I can't think of anything 'obvious', it looks annoying to calculate.
worn fox
1 - P(you dont draw an ace or a 9)?
pale kestrel
sure, of course, so the hard part of the problem is calculating P(no A or 9, drawing 1 card from 37) and then the same for 36
worn fox
oh is the issue here that you dont know where the 9's are
pale kestrel
Yes, so they can be among those 8 other cards as well.
Oh actually maybe its not as ugly as I thought
worn fox
it does seem like cases on where the 9s could be is your best bet
pale kestrel
35/37 * 43/45 I think this works actually?
I was thinking combinatorically before rather than just probabilities
So I reckon the final answer is 1 - (35/37 * 43/45) * (34/36 * 42/44)
,calc 1 - (35/37 * 43/45) (34/36 * 42/44)
ocean sealBOT
Result:
0.18511693511694
That working look right? 
worn fox
im not seeing the cases in your work
there should be 3 cases: both 9s in the 37, one 9 in the 37, no 9s in the 37
pale kestrel
I was thinking you could combine them, maybe im missing something
I was thinking you have:
37 cards
8 cards
2 9's in there somewhere
======
Probability of not drawing a 9 from the 37 card deck = 43/45 ?
worn fox
======
Probability of not drawing a 9 from the 37 card deck = 43/45 ?
that would be if you pulled from all 45
pale kestrel
But you basically are aren't you?
I mean sure, we can go chop it into the cases, but I think we end up with the same answer
worn fox
lemme check
pale kestrel
there should be 3 cases: both 9s in the 37, one 9 in the 37, no 9s in the 37
Also its a bit complex isn't it? You also have to take into account the probability of each of these happening
that looks really annoying haha
45 choose 37 is your space
and ig you just count
43 choose 35, 43 choose 36, 43 choose 37
pale kestrel
there should be 3 cases: both 9s in the 37, one 9 in the 37, no 9s in the 37
so 43C35 / 45C37, 43C36 / 45C37, 43C37 / 45C37 respectively are the probabilities of each of these
worn fox
eh yeah something fucky with my reasoning i get negative prob
pale kestrel
(35/37)(43C35 / 45C37) + (36/37)(43C36 / 45C37) + (37/37)(43C37 / 45C37)
I reckon its this (no 9 in one draw)
ocean sealBOT
The following error occured while calculating:
Error: Undefined symbol C35
pale kestrel
,w (35/37)((43 choose 35) / (45 choose 37)) + (36/37)((43 choose 36) / (45 choose 37)) + (37/37)((43 choose 37) / (45 choose 37))
ocean sealBOT
pale kestrel
,calc 43/45
ocean sealBOT
Result:
0.95555555555556
ehm i mustve done something funny
worn fox
yeah im not sure honestly sorry
pale kestrel
,w (2/37)((43 choose 35) / (45 choose 37)) + (1/37)((43 choose 36) / (45 choose 37)) + (0/37)((43 choose 37) / (45 choose 37))
ocean sealBOT
pale kestrel
No good still
hmm...
,w ((43 choose 35) / (45 choose 37)) + ((43 choose 36) / (45 choose 37)) + ((43 choose 37) / (45 choose 37))
ocean sealBOT
pale kestrel
doing something silly with my conditionals
45C37 ways to choose 37 cards from 45
we mark 2 of those 45 cards and consider 0, 1, 2 chosen
oh i have to 2x the 1 case
,w ((43 choose 35) / (45 choose 37)) + 2 * ((43 choose 36) / (45 choose 37)) + ((43 choose 37) / (45 choose 37))
ocean sealBOT
pale kestrel
,w (2/37)((43 choose 35) / (45 choose 37)) + 2 * (1/37)((43 choose 36) / (45 choose 37)) + (0/37)((43 choose 37) / (45 choose 37))
ocean sealBOT
pale kestrel
righhht so yeah, its 43/45
,w (35/37)((43 choose 35) / (45 choose 37)) + 2 * (36/37)((43 choose 36) / (45 choose 37)) + (37/37)((43 choose 37) / (45 choose 37))
ocean sealBOT
pale kestrel
yh yh phew.
pale kestrel
So I reckon the final answer is `1 - (35/37 * 43/45) * (34/36 * 42/44)`
And then back to this.........
"Probability of no A or 9 from a single draw"
uhhhhhhhhhhhhh these should be independent right
justifying 35/37 * 43/45 multiplied
no wait maybe not
gah
brain
chrome salmon
Don't worry
pale kestrel
yeah you cant both draw an A and 9 in a single draw
not independent
damn that is hella annoying.
how does one do math again 
I think I need to approach this by considering the 45 card deck at all times...
chrome salmon
What are the three cases you made
pale kestrel
Yeah I can also do that I guess
I was originally hoping to get this done without chopping into cases
0 1 or 2, 9's in the 37 deck are the 3 cases
chrome salmon
It's atleast one ace or atleast one 9
pale kestrel
,w (4/37) * ((43 choose 35) / (45 choose 37)) + (3/37) * 2 * ((43 choose 36) / (45 choose 37)) + (2/37) * ((43 choose 37) / (45 choose 37))
ocean sealBOT
chrome salmon
(37C1) is number of ways to get at least one ace righ
pale kestrel
not sure what u mean
chrome salmon
In how many ways can you get at least one ace
pale kestrel
Which part of the problem are you referring to
in one draw from the 37 card deck?
i mean, 2 cards in there are definitely an ace
so i guess.... 2 ways???
chrome salmon
in one draw from the 37 card deck?
In 2 draws
chrome salmon
Not 37C1?
chrome salmon
No distinction
chrome salmon
im confused where you're coming from with this
Do you have the final answer to this?
pale kestrel
im about to i think
chrome salmon
pale kestrel
,w 1 - ((33/37) * ((43 choose 35) / (45 choose 37)) + (34/37) * 2 * ((43 choose 36) / (45 choose 37)) + (35/37) * ((43 choose 37) / (45 choose 37))) * ((33/37) * ((42 choose 34) / (44 choose 36)) + (34/37) * 2 * ((42 choose 35) / (44 choose 36)) + (35/37) * ((42 choose 35) / (44 choose 36)))
ocean sealBOT
chrome salmon
,w ((50 choose 35)(37 choose 1)+(51 choose 36)(36 choose 1))/((52 choose 37)(37 choose 2))
pale kestrel
omg thats hella annoying, how do i calculate this 
ocean sealBOT
pale kestrel
,w ((50 choose 35)(37 choose 1)+(51 choose 36)(36 choose 1))/((52 choose 37)(37 ...
whats this ?
the final answer should be approximately 20%
chrome salmon
Oh wait I think I may have missed some case
pale kestrel
,calc 1 - 1501/1665 * 17811/17501
ocean sealBOT
Result:
0.082529955817196
pale kestrel
,w 1 - ((33/37) * ((43 choose 35) / (45 choose 37)) + (34/37) * 2 * ((43 choose ...
this is wrong unelss i mistyped on calculator
I don't understand your reasoning though, could u explain it once uve corrected
1 - ((33/37) * ((43 choose 35) / (45 choose 37)) + (34/37) * 2 * ((43 choose 36) / (45 choose 37)) + (35/37) * ((43 choose 37) / (45 choose 37))) * ((32/36) * ((42 choose 34) / (44 choose 36)) + (33/36) * 2 * ((42 choose 35) / (44 choose 36)) + (34/36) * ((42 choose 36) / (44 choose 36)))
corrected something but not sure if theres more
(in the end tho, i was originally asking if there was a way to avoid this mess)
,calc 1 - 1501/1665 * 89/99
ocean sealBOT
Result:
0.18955925622592
k reckon this is the final answer
No wait 
guh still wrong, misthought the idea
Think I see your point. I have to split the overall situation into 3 cases
Not each draw into 3 cases. Cant assume independence
The entire problem lacks independence a lot
,w (1 - 33/37 * 32/36) * ((43 choose 35) / (45 choose 37)) + (1 - 34/37 * 33/36) * 2 * ((43 choose 36) / (45 choose 37)) + (1 - 35/37 * 34/36) * ((43 choose 37) / (45 choose 37))
ocean sealBOT
pale kestrel
Ok back. Reckon this is the final answer.
theyre all so damn close as well
.close
glass atlas
help
glass atlas
I have this circle
and I've been trying to prove mathematically what the radius is
thing is the only proof I have is graphic
west girder
Pythagorean theorem
west girder
Oh
glass atlas
but how would you write your proof mathematically
here's what I mean
after fucking around, trying to deconstruct the circle in every which way imaginable
I finally figured out the line you have to draw is this one
but like how are you going to prove that the intersecting point between the line you drew and the horizontal line is aligned with the center of the circle
if that makes sense
west girder
Wdym aligned
west girder
He knows the radius
pale kestrel
If so they should consider rewording their original Q which says otherwise
west girder
I agree, I still don’t understand what they are asking
pale kestrel
Why don't you post the actual original problem?
glass atlas
can we go in a vc?
pale kestrel
It surely isnt this random diagram chucked at you
No ones going to understand
None exist.
glass atlas
worn fox
but like how are you going to prove that the intersecting point between the line...
are you asking how to prove your red diagonal line intersects the black horizontal line at x=0?
west girder
You don’t need what you are doing to solve it
glass atlas
No I'm mean like probably don't but it definitely helps me.
west girder
We can’t really help you since we don’t know your question
glass atlas
I wished I had the slightest ounce of mathematical vocabulary
I'll return with a more proper explanation.
.close
lone heartBOT
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Available help channel!
ocean glacier
how do I take the red integral? (so that it doesn't use the integral function) https://www.desmos.com/calculator/wsc7wg1ilx
lone heartBOT
how do I take the red integral? (so that it doesn't use the integral function) h...
@ocean glacier Has your question been resolved?
lone heartBOT
@ocean glacier Has your question been resolved?
pine kettle
how do I take the red integral? (so that it doesn't use the integral function) h...
do you have to not approximate
ocean glacier
do you have to not approximate
yes
lone heartBOT
@ocean glacier Has your question been resolved?
lone heartBOT
@ocean glacier Has your question been resolved?
vapid kettle
I need help finding the area on 55. And also finding area between two functions in general.
opal pine
Do you know what the general form should be for area between two functions?
lone heartBOT
@ocean glacier Has your question been resolved?
somber salmon
You need to find integral
I think you need to find on the both side like (-2;0) n (0;2)
And plus them
Or if they are the same you can make it *2
empty igloo
HOW TO SLOVE 6 AND 7
random mauve
HOW TO SLOVE 6 AND 7
Oh this ones ez.
If u want to take hcf, u just take hcf of numerator/ LCM of denominator
I.e hcf{60,36}/LCM {17,34}
?
english
lone heartBOT
@ocean glacier Has your question been resolved?
raven rover
how do I take the red integral? (so that it doesn't use the integral function) h...
Idk if the red function has a nice antiderivative
ocean glacier
Idk if the red function has a nice antiderivative
f
raven rover
ye
storm shoal
i dont think this one has a solution but maybe it does. And its say my first assumption is right is their a difference between undefined vs no solution
naive valley
the expression in parentheses is the sum of a 3x2 matrix and a 2x1 matrix.. this is undefined
empty igloo
I.e hcf{60,36}/LCM {17,34}
ty bro
limpid turret
@ocean glacier the real question is why you want to. What's your goal here?
noble fjord
im pretty sure you switch the x and y
true sinew
genius
alpine sable
Yes you do.
Once you switch the X and Y, solve for Y and then you got your inverse function. @true sinew
lone heartBOT
guys
Please read #❓how-to-get-help
lone heartBOT
@ocean glacier Has your question been resolved?
gentle osprey
#help
gentle osprey
Limits
I just simply put the numerator into 2 + 3 sinx/x and denominator into 5 - cosx/x
Since sinx/x =1
2 +3(1) for the numerator but for the denominator i don't know how to simplify further.
brave kayak
is it even asking for simplification?
i would sub a really large number for x and prove its value
naive valley
sinx/x approaches something even nicer when x->inf, and so does cosx/x
gentle osprey
is it even asking for simplification?
I think so simplifying and input the limit or i maybe wrong
raven rover
As x -> infinity, what do sin x, cos x, and x approach?
brave kayak
sin(x)/x approaches 0 from the negative
cos(x)/x also approaches 0
it would be 2/5
since the sin(x)/x and cos(x)/x approach 0 as x approaches infinity
naive valley
sin(x)/x approaches 0 from the negative
actually oscillates between + and - all the way to infinity, but you're correct that it approaches 0
brave kayak
if you sub in a large number for x, you get a negligible negative number
naive valley
,w plot sin(x)/x from -1000 to 1000
ocean sealBOT
naive valley
for positive x, sin(x)/x has the same sign as sin(x), which oscillates all the way to infty
doesn't really matter for this problem, just a side note
gentle osprey
Ok
vague coral
brave kayak
yeah my problem is that no matter the number i put for x i always get a negative in sin(x)/x
naive valley
yeah my problem is that no matter the number i put for x i always get a negative...
try say x = -pi/2 + 1000000pi 😁
oh wait, you want a positive
brave kayak
yes
brave kayak
wait we are dealing in radians?
naive valley
yea, we are math people not schoolchildren haha
radians or go home
j/k, if degrees then you can use 90 + any integer multiple of 360
brave kayak
no but for degrees no matter how big x is it is a negative
naive valley
>> x = 90 + 1000*360;
>> sind(x)/x
ans =
2.77708350690105e-06
ok thanks
lone heartBOT
@gentle osprey Has your question been resolved?
woeful parcel
lone heartBOT
woeful parcel
hey, am struggling with this problem, i tried to used vertex formula to find the a but i cant since i dont know what b is
woeful parcel
At the end it meant to say: ax^2+bx+c
i know the leading coefficent is going to be negative due to the intersections
lone heartBOT
@woeful parcel Has your question been resolved?
queen river
you find the formula first
using completing square
because you know the vertex
like this
,rotate
ocean sealBOT
woeful parcel
ok, how do you solve for a then or for n
woeful parcel
nope
brave kayak
do simultaneous equations with the three variables
x=1, x=-1 and x=3
it'll take a bit
woeful parcel
i dont know what this is
queen river
lets sub -1 or 3 in the equation
queen river
ok
queen river
ive find the equation right
Then we sub -1 to the equation
like this
then find a b c
should be y=
lone heartBOT
@woeful parcel Has your question been resolved?
spare frost
lone heartBOT
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@spare frost Has your question been resolved?
lone heartBOT
@spare frost Has your question been resolved?
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@spare frost Has your question been resolved?
lone heartBOT
lone heartBOT
Available help channel!
violet flare
hey
violet flare
here just for a logic check not a question specifically
If I had the word "zajak" (case is irrelevant) and i wanted to find the number of unique combinations of the letters in the word when 'z' is always first and 'k' is always last
would it be $\frac{3!}{2!}$
ocean sealBOT
Zouni
median oar
Yes, but why have you chosen 3!/2!
violet flare
as the z and k become irrelevant and 3! encompasses the cardinality of the letter set a,j,a and 2! is there to get rid of the non-unique combination of the a's
median oar
Good
violet flare
is that correct though
median oar
as the z and k become irrelevant and 3! encompasses the cardinality of the lette...
“Get rid” is kinda correct but not exactly right
Semantically wrong I’d say
You could think of it as 3 slots choose 2 for the places of a, or 3 slots choose 1 for the place of j
3C1 and 3C2 represents those 2 ways of thinking
violet flare
Ah ok
median oar
And you get 3!/(1!(3-1)!) = 3!/(1!2!) = 3!/2!
Or you get 3!/(2!(3-2)!) = 3!/(2!1!) = 3!/2!
median oar
Yes
You should also notice there are 1! Ways to arrange the j
There’s 2! Ways to arrange the a’s amongst themselves that’s why you divide by 2!
But you technically also divide by 1!
Suppose the word was zajjak
You’d instead get 4!/(2!2!)
hollow thicket
lone heartBOT
hollow thicket
getting a bit confused on how to solve the transformations
queen river
form g(x) to g(4x-3)
you know
first change from g(x) to g(4x) means
the graph contract by 1/4 time the original along the x axis
then g(4x) to g(4x-3)
which means the graph translated rightward by 3 units
second one will be like
hollow thicket
which means the graph translated rightward by 3 units
ah thanks
queen river
yes
queen river
No
After that
first contract
after that move rightward
the second one is like
from x^2 to x^2+ 2x
hollow thicket
mhm
queen river
change gx
to be (x+1)^2-1
Lets say y=p(x)
change from p(x) to p(x+1)-1
right?
,rotate
ocean sealBOT
hollow thicket
oh yeah understandable
queen river
ok
change from p(x) to p(x+1) means translate leftward by 1 unit
change from p(x+1) to p(x+1)-1 means translate downward by 1 unit
,w plot x^2
ocean sealBOT
queen river
,w plot x^2 + 2x
ocean sealBOT
hollow thicket
leftward by 1 and downward by 1
ahh i get it know thanks
queen river
No problem!
hollow thicket
No problem!
oh yeah one more question
queen river
what?
hollow thicket
in regards to b) the answer is this
hollow thicket
i was thinkuing because the image of x:
x' = 4x -3
x = x'/4 + 3/4
hollow thicket
Only when translate the graph first
ohhhhh
do it depends whcih transformation goes first
queen river
yes