a coin is flipped 3 times. what is the theoretical probability of getting heads all three times.
#help-0
halcyon dome
uneven dock
gray isle
consider introducing variables to represent the amount each person has
for convenience you could use Z and D
alpine sable
consider introducing variables to represent the amount each person has
Yep thanks
lone heartBOT
Available help channel!
alpine sable
lone heartBOT
alpine sable
for the blue line
is the slope for every 1 drop the conductivity increases by 111 µS?
sorry my handwriting is bad I can clarify anything
but the equation for the blue line is 96.7x+4200
so how did I get 111 since the slope is 96.7x
lone heartBOT
@alpine sable Has your question been resolved?
woeful pulsar
yeah, that's a question for yourself, how did you get 111mu S in the first place?
then again 111 and 96.7 are pretty close
alpine sable
my bad the problem was the grid was too small so I couldn't tell exactly what the numbers were
next pulsar
how do i find x_0 such that theres less than a 10% chance of X<0 ?
woeful pulsar
how do i find x_0 such that theres less than a 10% chance of X<0 ?
what do you mean "such that X>0"?
next pulsar
sorry my finger slipped on the enter key
woeful pulsar
it's a normal distribution, right?
next pulsar
yep, sorry about that, shouldve mentionewd i edited the original message
uhhhh, should i know what a z score is?
oh its just how many standard deviations away from the mean a point is?
in that case, a z score of 0 would be 16
woeful pulsar
0 would be 16 standard deviations away from the mean?
next pulsar
16 is 0 standard deviations away
woeful pulsar
oh wait, it's the other way around
wait a minute no
it's $x_0+2$ with a z-score of 0
ocean sealBOT
Element118
woeful pulsar
yeah there's something to do with inverse normal
next pulsar
oh! woops yes i confused the parameters together
yes x_0 + 2 has a z score of 0
ok so i am looking for Pr(X =< x_0) < 10
right?
woeful pulsar
wait but Pr(any event) < 10
next pulsar
0.1*
keep making silly mistakes
ive never dealt with inverse normal, would I just integrate the pdf for the normal distribution then use that to work out x_0?
i think i can integrate it if i change it to polar coordinates since it looks to me like the normal is of the form e^-x^2
maybe theres some bs in statistics that doesnt allow me to do that but i see nothing wrong with that approach?
woeful pulsar
you can't integrate it with elementary functions
the CDF can be looked up on a table
typically
so you can find the z-score of various values
next pulsar
whaaaaaaat, something so intrinsic in stats doesnt have a nice antiderivative??? O.O
man, im beat, i have no clue how to find x_0 here
woeful pulsar
Try finding what z score corresponds to a probability of 0.1
glass lichen
what are you struggling with...?
have you done an integral before?
it's the integral of x dx
coefficient but yeah.. it's just x^2/(4sqrt(3))
oh, cause it wasn't your channel...
sage tartan
mfw annexed my channel
alpine sable
Help
glass lichen
use a calculator...
glass lichen
,w calculate (456)^2
ocean sealBOT
glass lichen
yes
prime badge
no
void solar
maybe so
alpine sable
what
glass lichen
it's correct.
prime badge
no, 1 millions is not 10^5
void solar
no, 1 millions is not 10^5
wdym
prime badge
if it's correct, I want my old world back
glass lichen
so, like I said, yes it's correct.
void solar
lmao
obsidian crane
207936 = 2.07936 x 100000 = 2.07936 x 10^5
alpine sable
1 91/125
glass lichen
207936 = 2.07936 x 100000 = 2.07936 x 10^5
dont need echos btw
glass lichen
,w calculate (1.2)^3
ocean sealBOT
obsidian crane
that's it
alpine sable
is my answer right it's 1.2³ = 1 91/125, 1728, (6/3)³
Because scientific Notations or smth
glass lichen
is my answer right it's 1.2³ = 1 91/125, 1728, (6/3)³
I have... no clue what you're trying to say in your answer
why the fuck do you have a random (6/3)^3?
alpine sable
Basically it's only 1738
obsidian crane
is my answer right it's 1.2³ = 1 91/125, 1728, (6/3)³
That .. is not scientific notation
glass lichen
Basically it's only 1738
??
alpine sable
1.728*
glass lichen
1.728 in scientific notation is 1.728
alpine sable
yeah I know
obsidian crane
and scientific notation is only used when needed, how can you further simplify 1.728 ?
glass lichen
so what are you saying with the nonsense that is 1 91/125, 1728, 2^3?
obsidian crane
sure you can write 17.28 x 10^-1 but that's useless lmao
obsidian crane
alpine sable
so what are you saying with the nonsense that is 1 91/125, 1728, 2^3?
Photomath on crack
glass lichen
sure you can write `17.28 x 10^-1` but that's useless lmao
that's also not SN.
alpine sable
that's also not SN.
So it's 1.728
alpine sable
ight
obsidian crane
that's also not SN.
in Physics we sometimes use this to include helpful prefixes
sure it's not
alpine sable
#4 0.1024
#5. 5⁸
alpine sable
#4 0.1024
#5. 5⁸
@glass lichen My answer for 4 and 5
glass lichen
5's clearly wrong.
and in SN the number needs to be b/w 1 and 10.
so 4's also wrong
ocean sealBOT
alpine sable
@glass lichen so 0.1024 is wrong?
glass lichen
Said that, yes.
alpine sable
I thought it was the answer
glass lichen
it's not in proper SN
alpine sable
How is it supposed to be
glass lichen
check your notes for the rules of SN.
alpine sable
.close
void solar
lone heartBOT
void solar
Can someone quickly explain this
glass lichen
you add pi to it to do a 180 turn
void solar
you just add pi
So this dosent have a thing to do with Sin(x) being the same with Sin(pi-x)
well case closed, thanks
.close
copper tangle
For $k \neq 0$, find the value of $k$ such that $f(x) = kx^4 -2k^3x^2$ has a local maximum at $x = 1$.
ocean sealBOT
KaiML
bleak ridge
copper tangle
I found the derivative of f(x) , but I'm not sure where to go from there
bleak ridge
You'd want that derivative to have a zero at 1
copper tangle
derivative of f(x) being 4kx(x^2-k^2)
elder sedge
it has 2 properties
raw shard
f’’(x) must be greater than 0 at x = 1
i think that’s how it works, don’t remember for sure
if you just use the first derivative you don’t know if it’s a minimum or maximum
bleak ridge
copper tangle
Shouldn't it be less? because greater means concave up right?
elder sedge
less than 0
raw shard
oof
copper tangle
Oh ok
raw shard
oh yeah i thought they said minimum oops
copper tangle
So, I need to find second derivative. Give me a second while I do that
bleak ridge
A second has been given
copper tangle
huh
raw shard
oof
raw shard
yes
copper tangle
So I need k to be something so that f'' is less than 0 at x=1, so maybe I sub in x=1?
raw shard
yes
copper tangle
12k-4k^3,
bleak ridge
I'd prob start with the first derivative
raw shard
oh yeah
bleak ridge
Since it's more specific rather than less
copper tangle
Ok lemme do that
bleak ridge
It'll give you exact values to check with the second derivative
elder sedge
you want f" to be negative at x=1
because that would imply
the derivative function decreased to 0 (meaning your function was increasing 👀)
copper tangle
4k(1-k^2)
elder sedge
if that makes sense
copper tangle
Yea I get that
raw shard
my brain can’t comprehend lol
copper tangle
4k*(3-k^2)
So I ignore this rite
4k - 4k^3 = 0
and then
k=k^3
?
then k=1...
or -1
so then we check f'' right?
elder sedge
there is one more answer
copper tangle
0?
elder sedge
but your condition is k not 0 so works out
elder sedge
white swallow
(1+1/n)^n becomes 'e'
lone heartBOT
(1+1/n)^n becomes 'e'
white swallow
(1-1/n)^n but does this become some kind of 'e' too?
crisp grove
white swallow
I've never used wolfram alpha before but do you agree with Ryuzaki's answer?@raw shard
raw shard
yes
lone heartBOT
@vale hill Has your question been resolved?
oak chasm
How many people from P haven't submitted a response?
You seem to be adding all the nonsubmitters to Ps who travel by car.
But you can't add any Q nonsubmitters to Ps who travel by car because they're not Ps at all, so they can't be Ps who travel by car.
34 + 12 + 29 = 75 Ps have submitted a response. 94 - 75 = 19 Ps haven't submitted a response yet.
Those Ps can be added to Ps who travel by car to get 12 + 19 = 31 Ps who travel by car.
Then there would be 31 Ps who travel by car and 21 Qs who travel by car, so 21/(31 + 21) = 21/52.
white swallow
You must learn about functions, the x is probably the input u must give
if the problem doesn't specify the input, then you can usually test the function with simple inputs like -2, -1, 0, 1 and 2
that simply means they do the same thing but has a different name which are the f and g letters
for example f(x)=1+5x and g(x)=1+5x
the input which is (x)
you put a simple number like I mentioned above -2 -1 0 1 2
if I put -1 into the function it becomes f(-1)=1+5*(-1)
so that means the function takes -1 input and turns it into 1+5*(-1)= -4
you can graph it too
do you know how to graph x and y
function is just a fancy word
1+5x
input which is the number you give it
it can be any number
gray isle
f(x) = 1 + 5x
isn't really something you "solve"
cyan fog
Identify and explain one reason innovations and technology spread along the Silk Road.
lone heartBOT
@alpine sable Has your question been resolved?
unique fjord
is this channel occupied?
analog summit
Yeah
unique fjord
ahok
raven girder
Hello
raven girder
I have a simple function R -> R, x -> x²
how can I test if it's surjective?
this must be really simple but I can't see it
I tried writing down f(x) = x² but then got no further
.close
lone heartBOT
shell widget
@raven girder A function is surjective when its codomain = range. Here you can see that the codomain consists of all real numbers >= 0 but the range is R and so it isn't surjective.
Or take some y value in R for which there does not exist an x value in R, for example y = -3 which gives us -3 = x^2
lone heartBOT
Available help channel!
dark jewel
ehh I have no idea how to solve this question
lone heartBOT
ehh I have no idea how to solve this question
@dark jewel Has your question been resolved?
dark jewel
<@&286206848099549185>
lunar anchor
Hello, wtf do you want ?
dark jewel
ehh I have no idea how to solve this question
.
alpine sable
Hello, wtf do you want ?
please be respectful
lunar anchor
Sorry brah
steady trout
alpine sable
make a new channel
dark jewel
<@&286206848099549185>
uhh lemme try
thx
then?
I find more than the numbers in the options
cobalt palm
i'm literally studying this today
lmao
! is a factorial, basically multiplying it by any value below the number you give it
n is the total number, let's say students
r is the amount of groups of that number there are
so like let's say 19 students and you want to find out how many pairs of 2 you can make
2 is r, 19 is n and ! is factorial
just plug it into ur calculator and shabang
alpine sable
! is a factorial, basically multiplying it by any value below the number you giv...
“Multiplying” by ! is wrong language and a bad way to think about this
It’s like saying sin(x) is sin times x
glass lichen
I'm just portraying it in how i understood it
For n in N, n! := n(n-1)...(2)(1)
With 0!=1
dark jewel
just plug it into ur calculator and shabang
i am trying to solve this question with this equation but i think i am getting something wrong because i am finding very hign value numbers
cobalt palm
idk man, just try and logic check as much of it as you can, try doing it again fresh, if you still get the same result it’s likely either right or you’ve missed something
alpine sable
??
manic loom
then?
Say you have 15 students and want to discover how many pairs you can make with them. “r” will be 2 and “n” will be 15, then apply it to the formula and you’re done
15! Would be (15 x 14 x 13 … 2 x 1) for example
dark jewel
ok i got it
plain arch
Find the general solution to the following differential equation. I tried making a substitution of v = H/p but it didn't work. I am unsure what to do lol
Oh woops i didn't realise this is occupied uhhhhhh i hope you finished it
safe roost
I have a question
so i understand that there's 32 possibilities
now i could just write out all 32 possibilities and then count the ones that fit
but i want to understand the systematic approach to this
vale sapphire
Well, picture the sequence of coin tosses
That has an order
(H,H,H,T,T) fits the bill just as well (H,T,T,H,H)
And then notice that the only thing that uniquely characterizes these two sequences is the position of the "heads" throws
So, the number of ways to get exactly three heads is the number of ways to choose three spots for each "heads" where the order of the heads doesn't matter
In the general case, this is called a binomial coefficient
written $n \choose k$
ocean sealBOT
Syst3ms
vale sapphire
and pronouned "n choose k"
And n choose k is precisely the number of ways to choose k elements from a set with n elements, where order doesn't matter
In this case you may conceptualize it as choosing 3 elements from the set of all positions (1 through 5)
So in your case the number of ways to do that is 5 choose 3, which equals 10
safe roost
5 choose 3
safe roost
but uuuhh, hang on
let me try to grab this
as in understand
ok yes, i understand this bit.
so for the second answer, i could add up 5 choose 3, 5 choose 4, 5 choose 5?
safe roost
what i don't understand is... if i write 5 choose 3... what number does that become?
is that a fraction, or?
glass lichen
,w calculate 5 choose 3
vale sapphire
i mean, i'd have trouble picturing a fractional number of ways to choose elements from a set
KEK
,w calculate 5 choose 3
ocean sealBOT
safe roost
well thank god for the internet, but how would i calculate that "by hand" ?
vale sapphire
there is a formula but i want to give the intuition for it
glass lichen
$\binom{n}{r} :=\frac{n!}{r!(n-r)!}$
ocean sealBOT
Mosh
vale sapphire
my math teacher considers this a sin more or less
it hides the nature of the number a bit
anyway
say you want to choose r elements from a set with n elements
safe roost
so great - this formula is not in the theory i have to cover to answer these questions... it's later
vale sapphire
For the first element, you have n choices. For the second one, you only have n-1 options left. For the third one, n-2... For the r-th one, n-r+1 choices
So the total number of ways to arrange things is n(n-1)...(n-r+1)
However, in the definition we said that we didn't want to worry about the order
Which we do here
Since we choose each thing in order
So we have to divide by the amount of ways to order r elements, and that's precisely r!
So, the "true" formula is ${n \choose r} = \frac{n(n-1)(n-2)\cdots(n-r+1)}{r!}$
ocean sealBOT
Syst3ms
vale sapphire
But it turns out the numerator can be written as n!/(n-r)!
but that's a copout >:(
i'm slightly joking
safe roost
yeah so this is the first time seeing this... man i think our lecturer might just hate our guts
because he surely doesn't respect our time
vale sapphire
if you didn't know that, then well, get to writing the 32 possibilities
safe roost
hahaha yeah i am absolutely not doing that
vale sapphire
but this is the way you would avoid doing that
safe roost
thanks for showing me this
because i was looking at what the teacher is covering in the next class and this is not part of it
so they either made a mistake or want us to count all possibilities by hand
safe roost
@vale sapphire thanks for the help!
lone heartBOT
<@!193692307453771776> thanks for the help!
@safe roost Has your question been resolved?
lone heartBOT
Available help channel!
waxen arrow
I need help with question 5
lone heartBOT
I need help with question 5
bleak ridge
Do you know pyrhagorean theorem @waxen arrow
waxen arrow
Yes
bleak ridge
Just apply it in steps
waxen arrow
But that outer outside triangle is confusing me
bleak ridge
Wot about it
waxen arrow
Do I have to worry about that?
bleak ridge
Ye
waxen arrow
So what would I do?
bleak ridge
Well what do those two sides tell you about the third
bleak ridge
You know the third one by pythag
waxen arrow
Ok I think I get it now
So I would have to apply Pythagorean therom on the smaller triangle to find one side of the bigger triangle?
bleak ridge
Ye
waxen arrow
Alright thanks
bleak ridge
Np
lone heartBOT
@waxen arrow Has your question been resolved?
limpid flower
Hi, I'm trying to solve this problem: https://math.stackexchange.com/questions/3369782/sup-1-a-1-inf-a-for-inf-a-0 , but I didn't really get the guy's answer.
I don't really get the epsilon --> 0+ part, but anyway, I would like to solve it without it because I didn't learn about it in class.
After successfully proving that 1/inf(A) is a higher bound of 1/A I'm stuck at proving that it's the supremum. I tried to use the fact that there's an x in A s.t. x > inf(a) + epsilon but without success.
lone heartBOT
Hi, I'm trying to solve this problem: https://math.stackexchange.com/questions/3...
@limpid flower Has your question been resolved?
limpid flower
<@&286206848099549185>
remote heron
suggest #advanced-analysis
alpine sable
Solve this equation
jade canyon
Solve this equation
？
jade canyon
@alpine sable post on a new channel plz…
alpine sable
Which one
limpid flower
suggest <#576511214025310260>
What?
limpid flower
Hmm thanks, I can't access that channel though
jade canyon
why…
bright hedge
charred flint
how do you change the equation you see, x^2-2x-3, to x^2-3x-2
this'll be related to a line
inner sentinel
how is this not 0
jade canyon
why is 0
inner sentinel
cuz if u plug in 0 u get 0^0 which is 0
also when i graph the function it approaches 0 from the right
buoyant edge
It doesn't approach 0 from the right.
buoyant edge
Do it algebraically.
placid zinc
0^0 is like 0/0, basically a tell that you haven't solved the limit yet
inner sentinel
Do it algebraically.
ok i will but it is 1 right
buoyant edge
yeah
vale sapphire
0^0 is like 0/0, basically a tell that you haven't solved the limit yet
beyond that, it could equal quite literally anything
finding examples of it approaching anything in existence is quite interesting i'll admit
lone heartBOT
@limpid flower Has your question been resolved?
inner sentinel
this is - infinity right
placid zinc
This is not your channel, see #❓how-to-get-help
fair crater
,w (\sum_{k=1}^{n} 1/(k*(n-k)))
lone heartBOT
,w (\sum_{k=1}^{n} 1/(k*(n-k)))
ocean sealBOT
fair crater
Need some quick help. Can I assume $\psi^{(0)}$ is just the digamma function itself? That is,
$$\psi(x+1)=\int_{0}^{1}\left(\frac{1-t^{x}}{1-t}\right)\dd{t}-\gamma$$
ocean sealBOT
ShatteredSunlight
lone heartBOT
@fair crater Has your question been resolved?
loud cloak
lone heartBOT
loud cloak
does anyone know how tf i am meant to evaluate this
wolfram alhpa times out when i typed it in
this is how far i got before I ran into ln(0)
devout summit
Where did the "x" you wrote go?
charred flint
I used e, not sure why it timed out for you
loud cloak
Where did the "x" you wrote go?
thanks sm i will try again
Yeah i’m not sure
.close
fresh parcel
hey why isnt the derivative of e^(-kt) just e^(-kt)
lone heartBOT
hey why isnt the derivative of e^(-kt) just e^(-kt)
crude rose
hey why isnt the derivative of e^(-kt) just e^(-kt)
when u have e^u its always (e^u)*u'
fresh parcel
so e^u would be e^-kt right
crude rose
ya
somber spoke
lone heartBOT
somber spoke
how would i make a start on part iv
ive done parts 1-3 but cant seem to figure out 4
devout summit
What is the value of :\\$c_0x^{2n}+c_1x^{2n-1}+...c_{2n}$
ocean sealBOT
Euclid31415
devout summit
@somber spoke
devout summit
**Euclid31415**
If you multiply this by the expansion given in the question, we get another polynomial. Then, notice what the coefficient of x^{2n} becomes.
lone heartBOT
@somber spoke Has your question been resolved?
vital timber
I hope its ok if I ask here. Ishan hasn;t responded in 20 mins
Im doing problem 4
vital timber
lone heartBOT
vital timber
Im doing problem 4
This is what I have so far
Im not sure what step to take next
I solved for x and got (3/2) and solved for y and got (1/2)
and i said lambda = 1
i plugged this in and got 5 as a max
and -5 as a min
I plugged them into f(x,y)=3x+y
x and y dont work when I plug them into the constraint equation though
<@&286206848099549185>
lone heartBOT
@vital timber Has your question been resolved?
near saffron
Is this a valid proof? If f(x) = 1 if x is in the cantor set and f(x) = 0 if x is not in the cantor set, I want to show the integral from 0 to 1 of f is 0. Let f_n(x) = 1 if x is in c_n and 0 if x is not, where c_n is the sets in the construction of the cantor set, like for example c_2 = [0, 1/9] ∪ [2/9, 1/3] ∪ [2/3, 7/9] ∪ [8/9, 1]. Notice the integral from 0 to 1 of f_n(x) = (2/3)^n. Since f_n(x) >= f(x) for all natural numbers n and x in [0, 1], the integral from 0 to 1 of f_n is greater than or equal to the integral from 0 to 1 of f. The limit of the sequence integral from 0 to 1 of f_n is 0 because (2/3)^n goes to 0, and then by the order limit theorem the integral from 0 to 1 of f is less than or equal to 0. Since f(x) is always positive, the integral is greater than or equal to 0, which implies the integral equals 0. I'm unsure if this is valid because I'm assuming f is integrable, but it might still be valid because the proof might show f is integrable.
lone heartBOT
Is this a valid proof? If f(x) = 1 if x is in the cantor set and f(x) = 0 if x i...
@near saffron Has your question been resolved?
stable vigil
stable vigil
Don't ask in an occupied channel
dont care
wary stream
That's why you read the rules #❓how-to-get-help
wary stream
No
alpine sable
nobody will help you if you're like this
sly mantle
👢
small cypress
lol
lone heartBOT
@near saffron Has your question been resolved?
tawny dawn
How do I factor x(x-3-40)=0
lone heartBOT
How do I factor x(x-3-40)=0
tawny dawn
How do you get that?
tawny dawn
x^2-3x-40x = 0
How do you get that?
tawny dawn
times the x with each value inside the brackers
How do you get eight and five?
placid creek
How to find x? I did some change of bases but It did not work on my end.
lone heartBOT
@tawny dawn Has your question been resolved?
sleek mist
Hello, can anybody help me with this problem? It wants me to solve for the values for [0,2pi]. The only thing I understood from my teacher is that your supposed to get cosine by itself and refer to the unit circle to find the values.
sleek mist
queen wigeon
Hello, can anybody help me with this problem? It wants me to solve for the value...
try setting cos(x) to a variable like y, then solving the resulting quadratic. then sub cos(x) back in for y and solve for x
lone heartBOT
@sleek mist Has your question been resolved?
lone heartBOT
lone heartBOT
Available help channel!
molten jewel
Quick question to help my understanding. Working on standard form to vertex form questions by completing the square. If I have say: y=x^2-8x+17 the b, (8) that I am diving by 2 is a -8 in this case? But since it becomes (-4)^2, it turns out positive?
lone heartBOT
Quick question to help my understanding. Working on standard form to vertex form...
@molten jewel Has your question been resolved?
fading zephyr
molten jewel
So it's -8/2 = (-4)^2 = +16, correct?
mortal mantle
Yup
waxen owl
Can I get some help on this problem.
lone heartBOT
Can I get some help on this problem.
placid creek
that is the original question
lone heartBOT
Available help channel!
fallow pagoda
how do i found an asymptote of a hyperbola ? like for examle
y = 4/x + 3
what would the asymptote be and how do i identify that
placid zinc
You'd want to know things about 1/x, then apply transformations onto it
,w graph 1/x
ocean sealBOT
fallow pagoda
what does that mean lol
next chasm
And x cant be 0 again, but you would move the graph 3 units up
placid zinc
Good call, you're right
fallow pagoda
right so would the asymptote be y = 3 ?
next chasm
what does that mean lol
So if at x0 for example f(x)=y, by stretching it would be f(x)=4y
x0-as in index
placid zinc
With those transformations in mind, the y = 0 asymptote becomes y = 3.
The x = 0 asymptote stays as x = 0
next chasm
Ye
next chasm
It dont
fallow pagoda
well the equation i gave was just an example im trying to understand how to identify and asymptote bc i have an exam coming u
so the y axis asmyptote is determined by the constant on the end
and the x axis asmyptote never changes?
ohh
unless
y = 3 / (x - 2 ) + 4
asymptotes:
y = 4
x = 2
is that right
.close
pearl jetty
A sensor node uses a radio (IEEE 802.15.4) that consumes 25 mA when transmitting or receiving. Assume that the battery holds a maximum of 2500 mAh with a required voltage level. The radio transmission speed is 250 kb / s. In practice, the radio is active during 4% of the time (duty cycle 4%), ie. the transmission speed is 10 kb / s on average. During the time the radio is idle, it is assumed that the energy consumption is approximately zero. Given these conditions calculate: After how long time does the battery need to be recharged?
pearl jetty
I would tell you what I calculated, but I think you would laugh
I think this is more of a physics question but idk
I got it to like 100 hours using thishttps://www.digikey.com/en/resources/conversion-calculators/conversion-calculator-battery-life
but since it is just 4% active it's actually 2500 hours
I think the reason it holds so long is because it is just a transmitter receiver sensor node (what is sensor about it) that is attached to a battery, no phone running any calculations or anything
lone heartBOT
@pearl jetty Has your question been resolved?
somber spoke
If you multiply this by the expansion given in the question, we get another poly...
im confused what do u mean?
pearl jetty
. . .
lone heartBOT
@pearl jetty Has your question been resolved?
modern lotus
I think the reason it holds so long is because it is just a transmitter receiver...
From a purely mathematical perspective these are the only useful information:
- The radio comsumes 25 mA
- The battery holds 2500mAh
- The radio is active during 4% of the time
All the other things are redundant.
So you first calculate how long it lasts if it's active 100% of the time
2500/25=100 hours
And then divide that by 4%
100/0.04=2500 hours
And if it is not the answer, please seek help in a…whatever field the problem is from…server
pearl jetty
I derived 2500H too
modern lotus
Is that wrong?
pearl jetty
I can't say since I don't know, but it was the same as I came up with
I do have a second question to this one
modern lotus
If the transmission speed or the standard it's using are irrelavent to energy consumption, then it should be 2500h
pearl jetty
yeah
How many bytes can be transferred from the sensor node, e.g. to a mobile phone, during a battery life if we assume that the sensor node only transmits and does not receive data?
I derived it to 450 GB
modern lotus
It transmits 10kb/s on average as given, so in 2500 hours, which is 2500*3600=9*10^6 seconds, it should be able to transmit 9*10^6*10=9*10^7kb of data
So if I have not mistaken, you multiply kb by 8 to get KB?
and then you divide 1024 for GB, I think?
pearl jetty
8 bit = 1 Byte
pearl jetty
Kilo1000 is mega and 1000mega is giga
pearl jetty
Mb = megabit and MB = megabyte
pearl jetty
Ehh?
modern lotus
The speed is given as kb/s so it's in kilobits
You have to multiply them by 8 to get Kilobyte isn't it
modern lotus
Yes
pearl jetty
80 kb = 10 KB
modern lotus
It's common to mix up the basic arithmetics so don't worry
And I'm 3 years into my computer science major
Which is embarrassing
pearl jetty
you are also using 2500 H when it should be 100H
since the radio is transmitting at all times
it would run out after 100 hours
so 100 H x 3600s x 10 000kb/s (or 1250KB/s if divided by eight) = 450 GB
lone heartBOT
@pearl jetty Has your question been resolved?
barren river
help, mainly asking for the third question
It asked for a real root and I have no idea how to get it
barren river
In another word im not sure if i did it correctly
nova wadi
do you mean for (iii)
barren river
yes
nova wadi
it's incorrect for (b) and (c)
barren river
right then how do i solve it
nova wadi
If it's asking for real roots, you can just look at how many times the curve crosses the x axis
nova wadi
you're correct for ii
for the number of x intercepts
ii and iii are asking the same thing
barren river
I kinda dont understand
nova wadi
pan4 bie2 shi
you need the equation or the graph
if you have the equation, you can calculate it
barren river
the b^2 4ac thing?
nova wadi
and if it is >0, then 2 real roots
yes
if = 0 then 1 real root,
if <0 then no real roots
barren river
ah alright thanks
nova wadi
yup np
barren river
how do i close this
nova wadi
uh idk lol
stuck jolt
barren river
.close
daring cairn
In what circumstances is equation (2) useful over equation (1) for solving the top optimisation problem
glass lichen
daring cairn
also just realised I'm missing an inverse sign on the inner bracket of (2)
rough acorn
oops we posted at the same time
daring cairn
if it helps, R is upper triangular as we are looking at the QR factorisation
One idea: For lambda sufficiently large, equation 2 allows us to ignore the term after the minus sign
<@&286206848099549185>
odd obsidian
lone heartBOT
odd obsidian
How can I solve this without L'Hopital's?
lone heartBOT
@odd obsidian Has your question been resolved?
nova wadi
interesting question, I can't figure it out yet but wondering what you have tried?
glass lichen
How can I solve this without L'Hopital's?
Multiply by the conjugate of the numerator
On the top and bottom of course
nova wadi
does that work with cube roots?
odd obsidian
Multiply by the conjugate of the numerator
I've tried that... it doesn't seem to work
odd obsidian
interesting question, I can't figure it out yet but wondering what you have trie...
I've tried just factoring it out, using the conjugate
glass lichen
Are you using the congujate or cbrt()+2?
glass lichen
That's not the conjugate in difference of cubes
glass lichen
Whats difference of cube factorization
odd obsidian
oh! is it (a-b)(a^2+2ab+b^2)?
glass lichen
Yes.
odd obsidian
= (a^3-b^3)
odd obsidian
The 2nd factor is the conjugate
Sorry, what does that mean?
the 2nd factor being the conjugate
as in, how would that work?
nova wadi
ohhhhhh makes sense now
glass lichen
You multiply top and bottom by the congujate
odd obsidian
You multiply top and bottom by the congujate
ah so I multiply by a^2+ab+b^2?
glass lichen
Yes.
odd obsidian
I see. That makes a lot of sense. Thank you!!
glass lichen
Simplify
glass lichen
(2-x)/(x-2)=?
odd obsidian
Ah right oops! My mistake, yeah it's plus 8
But then I still think I'm doing something wrong since it's supposed to be -1/12 but I'm getting -1/16
I'm not sure, I think I may have messed up the factorization
But thank you very much!!
.close
royal meadow
lone heartBOT
royal meadow
i think they're both linearly independent?
royal meadow
oh
oh fuck i'm a moron
yeah ok
for some reason i thought cos(2x) was 2sin(x)cos(x)
.close
compact orchid
Question:The length of a rectangle is increasing at a rate of 7cm/s and it’s width is increasing at a rate of 2cm/s. When the length is 20cm and the width is 15cm, how fast is the area of the rectangle increasing?
What’s wrong with my work!? Any help would be appreciated.
charred flint
area is just LW, and when you go from A to dA/dt you need to use the product rule on L and W
raven spade
need help
raven spade
uploading
wait
Yes
I don't know how to solve this
what do they mean with points and how to solve it?
I got this equation after taking the derivate with respect to time
but what to do farther what do they mean with points?
charred flint
points will just be spots on the x-y graph
you have the right first step, now you want that equation to become dx/dt=2dy/dt
although maybe it's a trick question because x^2+y^2-2x=-1 is a really weird graph
ocean sealBOT
charred flint
the graph is just the point (1,0) lol
raven spade
?!
charred flint
feels like a mistake in the question, but let's pretend it's a nice function that actually has a shape lmao
raven spade
Yeah I think it's a mistake
charred flint
you have 2xdx/dt + 2ydy/dt - 2dx/dt=0
raven spade
Yes
charred flint
and want the condition dx/dt=2dy/dt
charred flint
right so only a few values of x and y will satisfy the condition
and those values are your points
so moving dx stuff to one side and dy stuff to another
(2x-2) dx/dt = (2y) dy/dt
raven spade
Yes
charred flint
and the condition says 2x-2=1, 2y=2
charred flint
(2x-2) dx/dt = (2y) dy/dt
dx/dt = 2 dy/dt
I'm just matching the numbers in front of the dx and dy
charred flint
alright cool
raven spade
so If I got more than 1 x or more than 1 y that's mean I have multiple points
But because all the variable I have now is to the first power I only have 1 point right?
charred flint
right
raven spade
x1 = the first value of x
and y1 is the first value of y
and the same goes to number 2
Thank you
.cloes
.cloes
.close
delicate ridge
A study reported 36.5% episotomies in 10630 natural births.
Given a confidence interval of 95% calculate the margin of error's value for said confidence interval.
delicate ridge
Hi, so the given answer is 0.694%
With the given values I did:
Ends up as 1.96 . sqrt ( 0.365(1-0.365) / 10630 )
But it gives me 0.915%
Is the answer wrong or did I miss something?
?
<@&286206848099549185>
lone heartBOT
@delicate ridge Has your question been resolved?
cyan basalt
Hello. I cant figured out what is the primitive of a func and why i need it in integral calculus. Can y help me?
vale sapphire
I recommend this video (along with its associated series) by 3blue1brown
Antiderivative and primitive are synonyms (though the former is preferred in English)
If you want a quick and dirty answer, an antiderivative of a function f is a function F such that F'=f
But there's deep relations to integrals and the video gives an intuition for why that is
cyan basalt
Thx. I can imagine this like a derivative?
delicate ridge
Hi I don't wanna be a prick but this channel is occupied
vale sapphire
Thx. I can imagine this like a derivative?
on the contrary, the two are inverses of one another
but now let's vacate the channel please
fiery bronze
Mau has now the channel
cyan basalt
but now let's vacate the channel please
I cant send y a message, pls open chat. Sorry Mau, i cant write him :p
delicate ridge
yeah np
fiery bronze
channel is occupied.
short pumice
Sorry
fiery bronze
no worries
lone heartBOT
@delicate ridge Has your question been resolved?
wanton folio
on the contrary, the two are inverses of one another
That's not true at all.
vale sapphire
i mean yeah an integral isn't an antiderivative per se, but cmon cut me some slack
mighty brook
I feel as if this is a stupid question but: If there are 98,000,000 people, and I rank 4143 out of all of them, how do I put that as a percentile? i.e. I am in the top X percent of people.
delicate ridge
occupied channel but w/e; do 4143/98000000 then 1 - answ?
mighty brook
occupied channel but w/e; do 4143/98000000 then 1 - answ?
Appreciate it 🙏
raw shard
@delicate ridge repost your question so it’s at the bottom if you want
delicate ridge
Ok sure
A study reported **36.5% **episotomies in **10630 **natural births.
Given a confidence interval of 95% calculate the margin of error's value for said confidence interval.
With the given values I did:
Ends up as 1.96 . sqrt ( 0.365(1-0.365) / 10630 )
But it gives me 0.915%
Is the answer wrong or did I miss something?
lone heartBOT
@delicate ridge Has your question been resolved?
delicate ridge
I'll close the channel since i'll be watching atleti liverpool and can't keep up with the thread
.close
odd obsidian
lone heartBOT
odd obsidian
How could I solve this limit?
devout totem
L’Hopital’s
ancient saddle
because the sin(x) persists
Why does the sin(x) persist? The derivative of sine is cosine
devout totem
Top is just 3, bottom is $\pi\cos\pi x$
ocean sealBOT
Zachary
odd obsidian
yeah but then you plug in 2
devout totem
Luckily for us, $cos2\pi \not=0$
ocean sealBOT
Zachary
devout totem
No prob
lone heartBOT
crisp cosmos
hello?
lone heartBOT
Available help channel!
crisp cosmos
lightning wolf
lone heartBOT
lightning wolf
crisp cosmos
can you join the vc for one second
I NEED HELP
what is the difference between** i **and i
lone heartBOT
@crisp cosmos Has your question been resolved?
icy dagger
lone heartBOT
icy dagger
could someone please walk me through simplifying this?
+-
this is where im at now
i was able to simplify the square root
divide both 2s by 2?
icy dagger
drowsy sorrel
or is it requested to be calculaated
icy dagger
did u divide these two?