0, 6 and 1, 8 right?
#help-17
wild meteor
strange crater
it's asking for the x-intercept, too
wild meteor
it's asking for the x-intercept, too
oh crap im only suppost to use those
strange crater
for the x-intercept you should be solving 0 = 2x + 6
wild meteor
for the x-intercept you should be solving 0 = 2x + 6
yeah i still dont know how i get from that step to the next steo
(i sent another question to ask)
strange crater
just solve for x
strange crater
yeah
strange crater
the two intercepts
wild meteor
the two intercepts
idk what that is
strange crater
the x and y intercepts
wild meteor
what do you mean? that is a point
ohh mb
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north python
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north python
can someone help me with this, for some reason this isnt the answer
pale perch
your method?
vocal sleetBOT
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@north python Has your question been resolved?
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@north python Has your question been resolved?
north python
.close
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teal pelican
how do i find the perimeter of this
vocal sleetBOT
how do i find the perimeter of this
dull wind
how do i find the perimeter of this
notice that total length of red lines equals to yellow line
teal pelican
yes
vocal sleetBOT
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finite hatch
hi
finite hatch
some how my friend said im doing this wromg
can i plz have some help
he said i shouldve got 4 and -1
vital iron
did you try cross product?
vital iron
well when we cross product two parallel vectors the resultant is zero since the angle between them is 0
and sin0 = 0
so you should cross product and equate with zero
vital iron
sorry im unaware of that property
finite hatch
because you know how parallel vectors
the red can just be multipled by a scale factor to be the same as blue
and they are parallel :D
strong grove
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rich sinew
Question 15: Points A and B have coordinates (2,0) and (6,0) respectively. Points C and D have coordinates (a,4) and (-a,4) respectively.
a) Find the equation of line AC in terms of a.
b) Find the equation of line BD in terms of a.
c) Find the coordinates of P the point of intersection of line AC and line BD in terms of a.
d) Prove that P lies on the line x+y=4
vocal sleetBOT
Question 15: Points A and B have coordinates (2,0) and (6,0) respectively. Point...
rich sinew
i dont really want the answer for this
its a question on an assessment task
however i have spent an embarrasing amount of time on this question and am begining to question whether its possible or not
so before i spend an even more embarrasing amount of time on it, i wanted to come here and make sure its possible
dull wind
can you draw a coordinate system with the points A, B, C, D for me
rich sinew
can you do that with unknowns?
parts a b and c all make sense to me
but there is no way P is on that line
rich sinew
remember i dont want the answer
i just need to know if its possible or not
part d) in particular
dull wind
after you find the coordinates of P
dull wind
check if it satisfies x+y = 4
rich sinew
not unless a=0
rich sinew
x=a, y=4
it satisfys both equations
but it dosent lie on x+y=4
so im wondering if i made a mistake somewhere or if the question is written wrong
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sly imp
I calculated the total number of possibilities and subtracted from it the number of possibilities where 2 girls do sit next to each other.
The real answer however is 1440, so ig I calculated the number of of possibilities where 2 girls do sit next to each other as too high? How so?
vocal sleetBOT
I calculated the total number of possibilities and subtracted from it the number...
sly imp
Don't need the answer to the question itself, just why my calculation was wrong
wary fiber
Don't need the answer to the question itself, just why my calculation was wrong
where did you get those numbers from? If you explain your thought process, I might be able to help.
sly imp
I calculated the the number of ways 3 girls could be randomly selected and arranged in 2 spaces as 3p2, then multiplied it by 6 cuz these 2 linked spaces can be in 6 spots in total, then multiplied that by 5p5 cuz the rest 5 people can be arranged in 5 spaces randomly
Now that I think about it, another girl could still be on either side of the 2 girls standing next to each other by this calculation, or just one side when the linked spaces are on either of the farthest edges
How would I account for that by this method?
wary fiber
I calculated the the number of ways 3 girls could be randomly selected and arran...
are you sure you calculated all possible permuations?
sly imp
Apparently calculated it as too high since subtracting it from the total gives a lower answer than the correct one
wary fiber
true
also you could just try another method overall since this may lead to some errors
sly imp
Let me phrase it this way: How could I calculate the number of possibilities where only 2 girls are standing next to each other in this situation?
Since that's what I'm trying to subtract from the total number of possibilities
wary fiber
Let me phrase it this way: How could I calculate the number of possibilities whe...
wait 4320 is where you have made an error
sly imp
Yeah
wary fiber
4320 possible combinations occur when 3 girls and 5 boys are arranged in a row such that all 3 girls are always together
however in your question it says 4 boys not 5
sly imp
Now that I think about it, another girl could still be on either side of the 2 g...
Yeah I figured that out later
sly imp
Let me phrase it this way: How could I calculate the number of possibilities whe...
But how do I get the correct answer for this then?
desert flax
I am stuck on number two I don’t know how to find the variables after finding the equations
vocal sleetBOT
I am stuck on number two I don’t know how to find the variables after finding th...
twin meteorBOT
desert flax
<@&286206848099549185>
desert flax
Hello
idle pasture
One sec
desert flax
Ok ok
idle pasture
Alr so the each Sold amount of t Shirts and hoddies IS X
X IS a variable for an unknown number
I got 95 t Shirts and 94 Hoodies Not completly Sure If thats true
Bassically did (5680 / 20€) - 189
Which Is 95
And how i calculated the hoddies should be clear
vocal sleetBOT
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raw flax
Hello
raw flax
I need help with integrals
vast shale
dm me
digital sedge
vocal sleetBOT
digital sedge
i need help with these type of equations
ik u do 0=x-0.15x^2
but idk what to do after that
pliant lintel
but idk what to do after that
Are you aware of what method you use to find these answers? For example, do you use the properties of a parabola to determine the vertex?
For part B we can use the information given in the picture that the arc of rosies path is a parabola with a vertex x value that can be found by using the vertex formula -b/2a
ring a bell?
pliant lintel
For part a, we know that the points of interest are the points at where rosie is touching the ground
therefore, when h(x)=0
digital sedge
yes
pliant lintel
So if you set h(x)=0 and solve for x, that will give you 2 points where rosie is on the ground
so you know those values are for where she first jumps, and where she lands
where she lands is your distance
setting h(x)=0 you get x-0.15x^2 = 0
you may factor that and set each factor to 0
youll get one factor that states x=0, thats the value where rosie started, but the other value you get is where she landed (the distance)
This works because h(x) is equal to 0 when the object is at ground level
and since we know that the only time rosie is at ground level is when she jumps and when she lands, those are the 2 values youre looking for
digital sedge
yes so x-0.15x^2=0
pliant lintel
correct
digital sedge
and x1 will be 0
pliant lintel
right
digital sedge
but idk how to do the equation
pliant lintel
so we have x-0.15x^2=0
we see we can factor an x out of the left side
giving us x(1-0.15x)=0 right?
pliant lintel
So you see, one of the values of x would be 0 which is where rosie started on the ground
setting the other factor to 0 would give you the other point she was on the ground which has to be where she landed
so what do you get when you do that
pliant lintel
Thats right
digital sedge
and 0.15x=1
pliant lintel
right
digital sedge
then 1/0.15
pliant lintel
Exactly
digital sedge
= 6.7
pliant lintel
rounded to the nearest 10th yes
digital sedge
yeah its like 6.666666
and if i do b
i want middle of the jump
so 6.7/2?
h(3.35)= 3.35 -0.15*3.35^2 ?
pliant lintel
Close, but that wont give you the exact answer because youre plugging in a rounded value
usually you want to plug in an exact value
so it would be 6.66666/2 and then you plug in h(3.333)
you can also do this by recognizing that the given equation is a parabola, and knowing that the x value of the vertex of a parabola is -b/2a
So from here you can just see that b=1 and a=-0.15
So you can calculate -1/(2*-0.15) and get your x value that way
then plug that x value in for the equation
digital sedge
i got 1.7
pliant lintel
Correct, we use the same method in the last one to solve for b
We see that the width is given by where the parabola touches the x axis
and we know that at the x axis, x=0
So we know that h(x) is going to be 0 at these 2 points, the start and the end
digital sedge
0=-0.0023x^2+40
pliant lintel
Right, we see that we cant factor an x out there so what do you think we should do
digital sedge
factor something other than x maybe
pliant lintel
You could but that wouldnt get you both values of x
Since we cant immediately factor an x out here to get both roots, we must do it a different way
We could isolate x instead by getting the 40 to the other side
digital sedge
so -0.0023x^2=40 ?
pliant lintel
=-40*
digital sedge
oh yeah
pliant lintel
Then from there we can further simplify to isolate x by multiplying both sides by -1 to get rid of the negatives
so we get 0.0023x^2 =40
Then to further isolate x we just divide both sides by 0.0023
digital sedge
x^2= 17391 ?
pliant lintel
Yes, but depending on how specific you need your answer, you need to not approximate until you get to the final answer
x^2 ~ 17391
digital sedge
17391.30435
pliant lintel
That is still an approximation but closer to the values we want
digital sedge
thats as far the calculator we use went
pliant lintel
What must we do do get both values of x here
digital sedge
sqrt17391.30435
pliant lintel
right, you square root both sides
digital sedge
then x = plus minus
pliant lintel
Exactly
digital sedge
~264
pliant lintel
Correct, however since you approximated the square root, your value is rounded to the nearest whole number
Rounded to the nearest 100th, the answer would be 263.76 but depending on what your instructor wants, your answer might be fine
digital sedge
yeah cheat sheet says 264
pliant lintel
just make sure in the future, to not approximate values until the final answer
if they want you to round to the nearest 10th or 100th, rounding values before your final answer will skew your final answer
digital sedge
yeah
if i get -wtvx= -wtvy
can i times it with -1 and get both positive
like we did before
na nvm
thanks
ur good at explaining
.close
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latent magnet
Can you take the laplace transform of the unit step function alone? The definition usually is L{f(t-a)u(t-a)} = e^-as F(s) where F(s) = L{f(t)} but in the ode I'm trying to solve the right hand side is just 1 - u(t-2) and idk how to take the laplace transfrom of that
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Can you take the laplace transform of the unit step function alone? The definiti...
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latent magnet
<@&286206848099549185>
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latent magnet
<@&286206848099549185>
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vernal isle
An aircraft weighing 238,000 Newtons drives at 40 degrees to the horizontal with a speed of 21.5 meters per second. Compare the load factor at this instant with the load factor at the lowest point in the pull-out. Calculate also the aerodynamic lift at both instances. The radius of turn is assumed to be constant at 12.2 meters.
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An aircraft weighing 238,000 Newtons drives at 40 degrees to the horizontal with...
vernal isle
what is load factor
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unique glade
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unique glade
Trying to find value of Tan(22.5degrees)
I did it twice and I keep getting the same answer, but on the website it says the answer is
Squareroot 2, - 1
I get squareroot 2, -2
vocal sleetBOT
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unique glade
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unique glade
Answer is what I have, but the 1/2 is negative
What did I do wrong?
Trying to find sin 9pi/8
outer warren
in the half angle identities,
there is a +- for the root
here it doesn't say that both signs are valid, but that you should determine the appropriate sign based on the angle
i.e you should identify what quadrant 9pi/8 is in
and whether sin is positive or negative in that quadrant
unique glade
idk if im losing my mind
but i keep getting it to quadrant 1
pi/4 9 times
gets me back to quadrant 1
outer warren
you want the location of the original angle for the final sign
unique glade
9pi/8
outer warren
yes, what quad is that in
unique glade
quadrant 3 i think
outer warren
yes
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fading spruce
Hi, i need some help on a proof. I wanna show, that the following matrix is positive definite.
vocal sleetBOT
Hi, i need some help on a proof. I wanna show, that the following matrix is posi...
fading spruce
this is in essence the statement i have been trying to proof. Idk if there is an easier way
this is where im stuck
<@&286206848099549185>
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@fading spruce Has your question been resolved?
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@fading spruce Has your question been resolved?
fading spruce
<@&286206848099549185>
thin vale
is the rest of the matrix zeroes?
fading spruce
yes
thin vale
the dimension is arbitrary?
fading spruce
i tried this, but it doesnt work
at least not in a way i could think of
btw technically im supposed to check for every n wether A represents an inner product
thin vale
have you shown all but positive definiteness
fading spruce
A is obviously symmetric, and im pretty sure its positive definite aswell, but i have no idea how to proof that
yes
thin vale
have you tried showing that <Ax, x> >=0
fading spruce
i got this by explicitly calculating x^T A x
fading spruce
have you tried showing that <Ax, x> >=0
im not sure, what you mean?
thin vale
i got this by explicitly calculating x^T A x
What is x^T A x = ?
thin vale
im not sure, what you mean?
if you show that the dot product of Ax and x is >= 0 then A is PSD
fading spruce
A is positive definite then x^T A x > 0
thin vale
A is positive definite then x^T A x > 0
another equivalent is the above I just gave
fading spruce
this expression is what i got
thin vale
this expression is what i got
that has a > sign in it, how did you get that from computing x^T A x 😭
fading spruce
thin vale
are any of the x_i negative
fading spruce
in order for this to be 0, the absolute value of the second term must be smaller than the first term
fading spruce
are any of the x_i negative
x_i is an arbitrary real value
thin vale
ah
fading spruce
i played around with the x_i's a bit but i could proof the inequality
thin vale
maybe rewrite the second sum to be to n
and subtract off the nth term
so that way you can combine the sums
fading spruce
already did that
i dont see how that helps tho
because intuitively, this inequality must be true, i just cant get to the point of actually proving it and it annoys me
thin vale
you have to take the absolute value
of the x_i x_i+1 sum
then you want to show the difference is > 0
and then you can use the triangle inequality
the absolute value of the sum will be less than the sum of the absolute values
then you can combine them as you did above, or perhaps differently as I recommended (not sure if either way is better)
but you could reindex the second sum instead of the first
fading spruce
everything you just explained i already did
thin vale
Okay, I'm just spitballing ideas and in the last pic you sent I don't see that stuff
sorry it hasn't worked
thin vale
im not criticizing you, im just very frustrated with that problem
have you considered if something might be telescoping
red bear
what is happening
fading spruce
i cant get this to work because of abs(xn) > abs(xn+1)
red bear
uh yes this looks right
thin vale
what is happening
my doubt linked you to the relevant image sir
fading spruce
cauchy schwarz only works if thats already an inner product no?
red bear
actually something more is true, any $\sum^n_{i=1}x_i^2 \ge \sum^n_{i=1}x_ix_{\sigma(i)}$ for any permutation $\sigma$ of ${1,2\dots,n}$
twin meteorBOT
Bair
red bear
cauchy schwarz only works if thats already an inner product no?
you can form an inner product between the vectors $(x_1,\dots,x_n)$ and $(x_{\sigma(1)},\dots,x_{\sigma(n)})$
twin meteorBOT
Bair
twin meteorBOT
Bair
red bear
bruh why not
fading spruce
we have to follow our script and the cauchy schwarz inequality comes after that ex
red bear
well im not sure how to help you then
fading spruce
red bear
im not sure if its the only way, but i think it is by far the easiest and cleanest and i wouldn't really want to think of a different way
red bear
how do you get to this tho
cauchy schwarz on the two vectors i painfully typeset just now
fading spruce
okay wait let me write it down
just based on this
i wouldnt know how to get from this to the inequality that i want to show
red bear
ok so the left hand side is the square of the sum you want minus one of the terms right
fading spruce
the inequality is flipped
red bear
both terms in the right hand side are the same, since the vectors have the same magnitude
so you just square root both sides
and you are done
fading spruce
maybe im just being stupid but that doesnt make sense to me
red bear
what are you confused about
fading spruce
oh wait
red bear
just plug in both vectors, and do some algebra and you will see
red bear
when
red bear
right
red bear
Cool
red bear
sorry, im very tired but that makes sense now
Also another way of thinking about is that you want to pair the largest numbers with the largest numbers to get the largest sum of products
So if I have 5 apples 3 bananas and 1 orange, and I want to assign prices to maximize profit, I should 3 dollars to apples, 2 dollars to bananas and 1 dollar to oranges
fading spruce
the problem wasnt that i didnt know it had to be true, i just didnt see a way to proof it but the cauchy schwarz inequality makes it very easy to proof yeah
i visualized it with 2 squares
but i didnt see the trick
red bear
@thin vale doubt clarified
thin vale
<@779131727338930196> doubt clarified
ty sir, I knew it had to be some kind of inequality you would know 😂
red bear
ty sir, I knew it had to be some kind of inequality you would know 😂
it was an inequality you knew too!
thin vale
it was an inequality you knew too!
i know cauchy schwarz but like u know cauchy schwarz lore
red bear
astronaut floating in space: wait it's all cauchy schwarz?
astronaut behind him with gun: always has been
fading spruce
i didnt look at anything later on in the script because usually youre supposed to use the stuff that you already know
but i was kinda helpless
red bear
i didnt look at anything later on in the script because usually youre supposed t...
actually now that i think about it you can probably get it from trivial inequality also
you can multiply both sides by two
and then move everything over to one side
and factor everything into squares
fading spruce
omg
i think thats how were supposed to do it
i just tralized that thats possible
thats way easier lol
i cant believe i didnt see that
im crying
red bear
I think this and the Cauchy shwarz are about the same level of difficulty though
red bear
,rotate
twin meteorBOT
red bear
well you need an extra x_1x_n term, but it only helps you
vocal sleetBOT
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inner patrol
Hi, I have this stats question. So, I am wondering about question 3b and 3c. I'm confused on the difference. My approach to 3b was follows:
Take $\mathbb{P}(|\bar{Y} - \mu| \le 0.5) = \mathbb{P}(-0.5 \le \bar{Y} - \mu \le 0.5$. and then by dividing both sides by $\sigma / \sqrt{n}$, we get the standard normal cdf. So, we get $2\Phi (\frac{-0.5}{\sigma / \sqrt{n}}) = 0.1$ by saying that n is large enough for it to approximate a normal distribution. thus, we want $\Phi (\frac{-0.5}{\sigma / \sqrt{n}}) = 0.05$ by plugging qnorm(0.05) into R, I get that $\frac{-0.5}{\sigma / \sqrt{n}} = -1.64485$. And then solving for n gives the approximation.
vocal sleetBOT
Hi, I have this stats question. So, I am wondering about question 3b and 3c. I'm...
inner patrol
hold on a sec
twin meteorBOT
theaveragejoe6029
inner patrol
wouldn't it be the exact same answer since in b we say n is bigger enought that we assume it to be a normal distribution and c we assume its a normal distribution
also sorry for my bad latex above
vocal sleetBOT
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inner patrol
Sorry to do this, but <@&286206848099549185>
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edgy ginkgo
hey
for this exercise I am asked to write down the first 3 terms of the Maclaurin series of the functions given to me
Then I am asked to find for which values of x does the Maclaurin series of that function absolutely converges
Here's what I've done
vocal sleetBOT
hey
for this exercise I am asked to write down the first 3 terms of the Maclauri...
edgy ginkgo
made a mistake
where I write Radius of convergence I meant Interval of convergence
the thing I'm mostly unsure of is when I have two separate series that describe a function, is the overall interval of absolute convergence their intersection?
(for example I found that for the first series the Interval of convergence is from -♾️ to ♾️ whereas in the second series I found that the Interval of convergence is from -1 to 1. Will the final interval of convergence be their intersection aka -1 to 1?)
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stark grail
vocal sleetBOT
stark grail
Question 8 pls
uneven belfry
flint topaz
What is the value of theta
vocal sleetBOT
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stark grail
No
stark lagoon
Working through some past paper questions on integrals, theyre just mcq but I struggle with some, mainly u substitution struggles me a bit
vocal sleetBOT
Working through some past paper questions on integrals, theyre just mcq but I st...
stark lagoon
1, 2, 3 are easy enough
4 ive got a bit done but got stuck
and the rest im lost
scenic ravine
for 5 use Integration by parts
robust python
doing the from (something) to (something) is easy enough u just find top minus bottom
stark lagoon
https://integral-calculator.com
thanks Ill give this a try
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nova pecan
Choose polynomials whose degrees are equal
vocal sleetBOT
Choose polynomials whose degrees are equal
nova pecan
help
outer warren
do you know the definition of "degree" in the context of polynomials
outer warren
look for the term with the highest power on the variable
that power will be the degree
robust python
Choose polynomials whose degrees are equal
Degree: The highest power (on a variable) of all the terms
Also if theres mutliple variables
u gotta add the degrees of each variable
on every term
nova pecan
look for the term with the highest power on the variable
that power will be the ...
tell me more in detail
robust python
basically what they just said
outer warren
there isn't much more detail for single variable polynomials
unless you don't know the definition of power
nova pecan
what should I do in such a situation?
outer warren
exactly as i described
robust python
tell me more in detail
What's the degree of k? Well k=k^1, so 1
What's the degree of 3k^4? 4
What's the degree of -2k^2? 2
What's the degree of 5? There's no variable, so 0
So you take the biggest
meaning ur degree is 4 for the top left
try doing that for every polynomial on there
until u find the same degree for 2
nova pecan
is that right answer?
outer warren
no
go through the powers term by term
what is the power of m in:
3m^2
3m^4
5m^7
7m^3
nova pecan
what is the power of m in:
3m^2
3m^4
5m^7
7m^3
this?
outer warren
yes
gray monolith
Hello
I just found this question online and when I tried to solve it I get a result different than the answers provided
The question is " what is the ratio of the colored area to the uncoloured area)
gray monolith
And By the way
This question assumes that pi is equal to 22/7
sharp frost
Hello
I just found this question online and when I tried to solve it I get a re...
have you found the length of square?
gray monolith
have you found the length of square?
I am not sure if I can get the length of the square
So I considered it as two triangles , the base equals 2r and the height of each equals r
You can also use the rombo area formula for the uncoloured area and you would still get 2r²
winter thistle
I am not sure if I can get the length of the square
So I considered it as two tr...
to make things easier, you can just assume the radius r = 1 here, it's ratio so it doesn't matter what r is (suggested by the question as well since it doesn't specified any value)
sharp frost
Is the answer c ?
winter thistle
I am not sure if I can get the length of the square
So I considered it as two tr...
to find the length of square, hint: Pythagoras Theorem
winter thistle
Is the answer c ?
that's what I got
sharp frost
You can also use the rombo area formula for the uncoloured area and you would st...
thats right
Area of uncoloured is 2r^2
sharp frost
Now area of coloured
gray monolith
sharp frost
,rotate
twin meteorBOT
winter thistle
why 2 pi r^2?
gray monolith
why 2 pi r^2?
I tried to find the coloured area
The circle area - the uncoloured area
winter thistle
I tried to find the coloured area
The circle area - the uncoloured area
area of a circle is not 2 pi r^2
gray monolith
area of a circle is not 2 pi r^2
Oh its Pi r²
winter thistle
yup
gray monolith
yup
So yeah the answer is C
Thank you @winter thistle @sharp frost
Sometimes I make stupid mistakes ( a lot of times😭)
winter thistle
Thank you <@690217572871831558> <@866605414154371083>
Sometimes I make stupid m...
np, it happens to all of us, don't mind
gray monolith
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quartz beacon
Does anyone know what the number 19 means here? When you calculate binomial distributions in this app geogebra it will generate a number for your distribution, but I was curious as to what it meant
vocal sleetBOT
Does anyone know what the number 19 means here? When you calculate binomial dist...
robust python
Does anyone know what the number 19 means here? When you calculate binomial dist...
whats verdeling
forgive??
oh
cyan talon
variable / distribution idk
robust python
distribution
quartz beacon
Distribution
cyan talon
it's just the number of steps I think
grim lotus
is it just be or is the distribution wrong
cyan talon
the doc just says "returns a bar graph"
grim lotus
shouldn't the max be at 10
grim lotus
oh maybe it's adding all probabilities
cyan talon
sum of probabilities = 19 sure
grim lotus
kind of a dumb thing to return cuz it's just 20-1 and 20 is ur input
quartz beacon
oh maybe it's adding all probabilities
mhm the true is for cumulating
grim lotus
sum of probabilities = 19 sure
no it's 1
cyan talon
yeah it's the cumulative distribution that's plotted
quartz beacon
Im just curious because the number looks random at sight
But surely there’s some reasoning
cyan talon
I literally cited the documentation of geogebra
that's why I think it's just a number of bars or some dumb stuff like that
just change the n a bit, we'll see
grim lotus
personally i don't like geogebra
quartz beacon
huh
cyan talon
because this command is missing an argument
there's like 3 different signatures to this function
autumn stratus
there's like 3 different signatures to this function
oh is there
quartz beacon
Yeah
grim lotus
what happens for 500
quartz beacon
451
grim lotus
maybe we should plot all values and do regression 
cyan talon
hehe
grim lotus
i think it's just a number where the probability is close to 1
quartz beacon
what n do u want
cyan talon
oh maybe it's adding all probabilities
ah you're onto something here
if you remove the true and just look at the pdf, the return is 1
why would that be useful
quartz beacon
wait what is it haha
quartz beacon
oh
grim lotus
wait that's just n - expectation
autumn stratus
maybe it's n - np = n*(1 - p)
oh thats it
quartz beacon
maybe it's n - np = n*(1 - p)
If you do this he’s one off
grim lotus
good question
cyan talon
well prolly the area under the bar graph
quartz beacon
kinda the estimated value for failure + 1?
cyan talon
+1 cause they included the last point for some reason
cyan talon
what have we become
quartz beacon
kinda the estimated value for failure + 1?
What about this
because estimated value for binomial distribution is n*p
cyan talon
yea sure
quartz beacon
I wish
grim lotus
this is why i don't like geogebra
quartz beacon
my teacher didn’t know so I got curious
cyan talon
fking docs
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forest lichen
How do i find the surface area of a shape like this?
(i already know what the base is, and the height is 6.)
vocal sleetBOT
How do i find the surface area of a shape like this?
(i already know what the ba...
grand rune
Multiply cross sectional are of base by the height
haughty arrow
Multiply cross sectional are of base by the height
Sir I belive that is volume 😂😂
haughty arrow
How do i find the surface area of a shape like this?
(i already know what the ba...
To find the SA you should first find the area of the top which will be the are of a triangle + a rectangle + a semi circle then multiply that by 2 for your top and bottom. To find the SA of the side find the perimeter and multiply it by the height After summing everything up you should find the surface area
grand rune
Sir I belive that is volume 😂😂
Yea
forest lichen
To find the SA you should first find the area of the top which will be the are o...
ohhh, wait that makes so much sense now, thank you alot.
haughty arrow
ohhh, wait that makes so much sense now, thank you alot.
Np
vocal sleetBOT
winter thistle
no
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west plaza
How do I determine the second differential to this general solution?
west plaza
I can't take the derivative of it twice
the differential should be sin(x)y'' - cos(x)y' = 0 but i have no idea how to get there
strange crater
why can't you take the derivative twice?
vocal sleetBOT
@west plaza Has your question been resolved?
west plaza
why can't you take the derivative twice?
because that's not the answer
if you do that and you plug it into the differential, you get -C2sin(x) + C1 = ?
hushed pewter
if you do that and you plug it into the differential, you get -C2sin(x) + C1 = ?
What?
winter thistle
if you do that and you plug it into the differential, you get -C2sin(x) + C1 = ?
how did you get that?
west plaza
how did you get that?
y = C2cos(x) + C1
y' = -C2sin(x)
y'' = -C2cos(x)
y'' + y' + y = ? the right hand side cant be 0 because of C1
then just plug the values in it
idk
winter thistle
well you shouldn't just plug it into y'' + y' + y, the general form of a second order differential is something like f(x)y'' + g(x)y' + h(x)y = 0, and if you plugged in y'', y' and y into the left hand side, and compare coefficients of C1 and C2, you should be able to find what f, g and h are
although, I've never seen a question asking what the 2nd order differential of a general soln is before, so I'm not 100% sure
vocal sleetBOT
Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.
dusk vale
?
tropic juniper
you can have it you're the goat anyway
vocal sleetBOT
you can have it you're the goat anyway
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orchid lodge
hi
orchid lodge
A bend in a road is formed from two concentric arcs with inside radius 𝑟 and
outside radius 𝑅, each of a third of a circle with the same centre. The road is
then formed of tangents to the arcs.
A cyclist cuts the corner by following an arc of radius 𝑥 which is tangent to
the outside of the road at its ends and tangent to the inside of the road in the
middle.
Prove that 𝑟 + 𝑥 = 𝑘 𝑅 for some number 𝑘 to be found.
can someone explaint his?
upper warren
😳
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frozen viper
helpo
heavy yoke
use trigonometry
crude arrow
let's think about this very hard
say we draw a equilateral triangle
of side length 2x
then we put a perpendicular bisector
frozen viper
perpendicular bisector is what
crude arrow
perpendicular bisector is what
show me your picture right now
frozen viper
10 | x | 60 degree
crude arrow
language man
frozen viper
how do I get the answer with no paper
dapper jay
dapper jay
how do I get the answer with no paper
what relationship exists between the angle, x and 3?
sin, cos, or tan?
frozen viper
tan
dapper jay
ok
twin meteorBOT
cwatson
frozen viper
opposite over adjacent
glacial osprey
look im all for trig but why dont we just use special right triangles
frozen viper
you guys could literally have just said 5tan(60)
glacial osprey
The point is that you learn how to do the problem so that you dont need to ask again
frozen viper
I learned that I could just do that
vocal sleetBOT
@frozen viper Has your question been resolved?
vocal sleetBOT
crude arrow
then we put a perpendicular bisector
!!!
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daring marsh
How do I solve this?
vocal sleetBOT
How do I solve this?
daring marsh
1/625
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cedar linden
still cant solve this
vocal sleetBOT
still cant solve this
cedar linden
\begin{align*}
\int_{1}^{2} \frac{x}{(x - 2) (x - 4)} & = \left[ x = (x - 4)A + (x-2)B \right] \\
&4 = (2)B \quad \Rightarrow \quad B = 2 \\
&2 = -2A \quad \Rightarrow \quad A = -1 \\
&= \int_{1}^{2} \frac{-1}{x - 2} + \int_{1}^{2} \frac{2}{x - 4} \\
&= - \ln|x - 2| + 2 \ln|x - 4| + c
\end{align*}```Juan
silk osprey
still cant solve this
bruh
cedar linden
not everyone are as smart as you 😦
silk osprey
try this
instead of the limit being 2
let it be some number b
and take the limit
as b -> 2
but use b instead of 2 in your anti derivative
so evaluate i from 1 to b
silk osprey
not everyone are as smart as you 😦
you should’ve told us you didn’t get it
so you have 2ln(x-4)-ln(x-2)
cedar linden
\begin{align*}
\int_{1}^{2} \frac{x}{(x - 2) (x - 4)} & = \left[ x = (x - 4)A + (x-2)B \right] \\
&4 = (2)B \quad \Rightarrow \quad B = 2 \\
&2 = -2A \quad \Rightarrow \quad A = -1 \\
&= \int_{1}^{2} \frac{-1}{x - 2} + \int_{1}^{2} \frac{2}{x - 4} \\
&= - \ln|x - 2| + 2 \ln|x - 4| \Bigg|_{1}^{B}
\end{align*}```Juan
cedar linden
you meant this
cedar linden
so i dont need to conver them into infinity
silk osprey
you used in partial fraction
silk osprey
so i dont need to conver them into infinity
mhm
cedar linden
can you correct my latex?
sharp frost
```latex
\begin{align*}
\int_{1}^{2} \frac{x}{(x - 2) (x - 4)} & = \left[ x = (...
Which part can't you understand?
cedar linden
Which part can't you understand?
when i determinate 2 and 1 I get ln|0|
so knief say instead of look for the B, just use the variable itself
sharp frost
when i determinate 2 and 1 I get `ln|0|`
Yeah, got it
cedar linden
to multiply
sharp frost
can you rewrite the -ln(x-2)+2ln(x-4)
Still it'll be ln 0 or ln infinity
silk osprey
still cant solve this
^
cedar linden
can you rewrite the -ln(x-2)+2ln(x-4)
$\ln | \frac{(x-4)^2}{x - 2}$
twin meteorBOT
Juan
twin meteorBOT
Juan
cedar linden
this is all i have
silk osprey
ok and what about the lower limit
like the 1
should be that -ln(9)
it doesn’t matter obviously but
yea
@cedar linden
so did you try to evaluate that limit
cedar linden
i tried to solve that fraction to see if i could eliminate the x - 2 but i couldnt
silk osprey
i tried to solve that fraction to see if i could eliminate the x - 2 but i could...
well what’s the limit as x->2 for x-2
and the limit as x->2 for (x-2)^2
cedar linden
for x - 2 is 0
and for the other one is 0 too
if im not in the same thing then just tell me
and i will close this
cedar linden
yeah
silk osprey
does that ring any bells
division by zero
with a nonzero numerator
what happens
when you divide by zero or take the limit and the denominator approaches zero
what happens to the quotient
if it helps
think of what happens if you took 1/0.0000000000001
if you divided by a reallllly small number
what would happen to the quotient
cedar linden
wont be indeterminate
mmm
you are telling me to do something
like
let B equal to 2.0000000001
silk osprey
really like B=1.999999999 but yes
because we’re coming from the left
the interval is 1 to 2
so we’re on the left side of 2
but it doesn’t matter
cedar linden
okay okay
silk osprey
well think of the graph of 1/x
cedar linden
so we can say
let b be equal to 1.99999999
twin meteorBOT
silk osprey
lets just look at it from one side
either one
as x goes to zero
what does 1/x go to
cedar linden
to 0.01
silk osprey
how’d you get that
don’t look at the numbers on the axes
just look at the behavior
silk osprey
yes
cedar linden
okay okay
silk osprey
think about it if i did 1/0.00000001 that’s really like multiplying 1000000000
so as it gets smaller and smaller
the quotient blows up
to infinity
does this make sense
cedar linden
yes
cedar linden
because from 1 to 0 there are infinite numbers
silk osprey
you have ln(2/0)
what does this approach
cedar linden
to positive infinite too
silk osprey
yes
because lim x->2 of (2/(x-2)) goes to infinity
so
ln(infinity)
is infinity
this make sense?
cedar linden
sure
silk osprey
no like fr
you understand that?
2/(x-2) was just the inside
of the ln
because we had ((x-4)^2/(x-2))
and i just simplified the numerator to 2
because x->2
cedar linden
sure we evaluated to limits so we got positive infinite
so we say ln (infinite) and thats equal to infinte
silk osprey
sure we evaluated to limits so we got positive infinite
so we say ln (infinite)...
mhm meaning that the integral is divergent or in other words it is not finite
cedar linden
yes
\begin{align*}
\int_{1}^{2} \frac{x}{(x - 2) (x - 4)} & = \left[ x = (x - 4)A + (x-2)B \right] \\
&4 = (2)B \quad \Rightarrow \quad B = 2 \\
&2 = -2A \quad \Rightarrow \quad A = -1 \\
&= \int_{1}^{2} \frac{-1}{x - 2} + \int_{1}^{2} \frac{2}{x - 4} \\
&= - \ln|x - 2| + 2 \ln|x - 4| + C \\
&= \ln | \frac{(x - 4)^2}{x - 2}| \\
&= \lim_{b \to 2} \, \ln | \frac{(x - 4)^2}{x - 2} | = +\infty \\
&= +\infty - \ln | (\frac{25}{-3}) | \\
&= + \infty + \ln | \frac{25}{3} | + C
\end{align*}
@silk osprey
whats your opinion
heavy yoke
remove the $$
twin meteorBOT
Juan
cedar linden
now?:D
silk osprey
if its infinite then there’s no need to add the constant terms
twin meteorBOT
silk osprey
and if you plugged in 1 you’d get ln(9)
it’s really infinity-ln(9) but that’s just infinity
and for a definite integral there is no +C
cedar linden
but my answer is correct?
cedar linden
what i do with the ln 25/3?
i did it because i evalute 1
what
wiat
i didt wrong
i just realilzed
xD
silk osprey
yup
silk osprey
and if you plugged in 1 you’d get ln(9)
^
silk osprey
no worries
cedar linden
so it will be
- infinite + ln(9)
silk osprey
doesn’t matter because it’s infinite
silk osprey
so it will be
+ infinite + ln(9)
no
infinity plus any number is stil infinity
so you can just write infinity
