spiral saffron
never mind i think i got it
#help-26
neon iron
Is derivative of continuous functions always continuous ?
topaz sinewBOT
Is derivative of continuous functions always continuous ?
vital relic
nope
ima try to think of one, but these are a pain to come up with
(ik the answer is no, though)
neon iron
But by the characterization of differentiation there exist g(x) which is continuous so that f'(x)=g(x)
vital relic
oh wait wait wait
Well ok
First of all
the derivative of a continuous function need not even exist at every point
You are aware of this right?
f(x) = |x| is continuous but not differentiable at 0
neon iron
You are aware of this right?
Yepp
vital relic
But even if it does exist, I believe it need not be continuous
thinking.......
I think the lurkers in #calculus are usually good with coming up with examples for stuff like this
vital relic
Is derivative of continuous functions always continuous ?
Oh and another point is, continuity is a necessary condition for a derivative to exist
So the question is better phrased as 'can we have a non-continuous derivative'
vital relic
vital relic
https://math.stackexchange.com/a/423279/243059
which allow examples like this
I'm unsure, you can try in #calculus or #real-complex-analysis
grim rover
topaz sinewBOT
grim rover
Hey, I need help with understanding this questio
How would G look if it's a subset of a product( which is made up of tuples?)
vale jacinth
Hey, I need help with understanding this questio
G_0={(g,1_G’):g from G}
And G_0’={(1_G,g’):g’ from G’}
grim rover
I mean like how do you know the identity is part of every tuple
vale jacinth
We just know
Now it’s given to you you can check whether they satisfy the condition now
grim rover
wait but i only know because you told me though
vale jacinth
I told you so you didn’t come up with it yourself, but you can still check it
Check it satisfies the condition
keen venture
Haha, you were doing this yesterday too. "But how would I have come up with the proof"?
It might be kind of unsatisfying, but yeah they show these proofs to you with the intention that you wouldn't have necessarily come up with it yourself
vale jacinth
It doesn’t matter.Me giving you the results is not different from you being given those results directly from the question. You can just pretend like the question gave you those and asked you to verify the properties
grim rover
It doesn’t matter.Me giving you the results is not different from you being give...
oh yeah i was just saying that because like if this was an exam question, how would i know that?
vale jacinth
Yeah verify that
Verify G times G’ is the direct product of its two normal subgroups G_0 and G_0’
vale jacinth
You will know that when you see it in exam next time
Since you have seen it before
I mean now, you have seen it, you can’t undo that. So next time you will also know this
grim rover
Yeah
well for property 1, (g,1_G') * (1_G,g') = (g,g') and that's an element of GxG'
Property 2 (trivial intersection) is also simple since G_0={(g,1_G’):g from G}
And G_0’={(1_G,g’):g’ from G’}
The only element that's possible in both has to be in both G_0 and G_0'
which is (1_G,1_G')
property 3 essentially using fact that they are both normal subgroups so
vale jacinth
Yeah
grim rover
(g1,1_G') * (1_G,g2') = (g1,g2') = (1_G,g2') * (g1,1_G')
and that's it i guess? you can switch around stuff(commute) due to the normal condition
vale jacinth
Yeah
grim rover
ah ok that was simpler than i expected then
vale jacinth
It is
grim rover
Thanks
vale jacinth
Np
grim rover
.close
topaz sinewBOT
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onyx light
topaz sinewBOT
topaz sinewBOT
@onyx light Has your question been resolved?
loud dawn
Rly
onyx light
Dumb question
whats anti symmetric mean
does it just mean not symmetric?
<@&286206848099549185>
topaz sinewBOT
@onyx light Has your question been resolved?
topaz sinewBOT
@onyx light Has your question been resolved?
loud dawn
It’s antisymmetric I believe
It’s not just “not symmetric”, it is much stronger than that - it says that there does not exist any distinct a,b such that aRb and bRa.
topaz sinewBOT
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snow pewter
how is x-y the square root [(x+y)²-4xy] ?
when we expand (x-y)^2 using the identity
don't we get x^2 - 2xy + y^2?
abstract wadi
Expand (x+y)^2
snow pewter
x^2 + 2xy + y^2
snow pewter
x^2 + y^2 - 2xy
snow pewter
Yeah but
abstract wadi
And we got x^2-2xy+y^2.
abstract wadi
Exactly.
snow pewter
but isn't (x+y)^2 = x^² + 2xy + y^2
abstract wadi
It is
snow pewter
we're using x^2 + y^2 here
abstract wadi
Sure.
snow pewter
?
abstract wadi
What?
snow pewter
So both of them are the same?
thorny flameBOT
Sakata Yaksha
abstract wadi
Is correct.
snow pewter
I understand this now
abstract wadi
Good.
snow pewter
But doesn't this go wrong because (a+b)^2 isn't a^2+b^2
abstract wadi
It is not, when did we say (a+b)^2 is a^2+b^2?
We said (a+b)^2 -4ab is same as (a-b)^2, don't forget that -4ab.
snow pewter
ah
abstract wadi
But doesn't this go wrong because (a+b)^2 isn't a^2+b^2
Also wait what man what?
$$(3m+6)^2 \neq 9m^2+36$$
thorny flameBOT
Sakata Yaksha
abstract wadi
Please, no god.
neon iron
Can someone help me solve a doubt?
I have these two samples:
$$ Sample1: (OK=90, KO=10) $$
$$ Sample2: (OK=86, KO=14) $$
I tried to assess with 95 percent probability whether the two accuracy rates (OK/(KO+OK)) are significantly different.
To do that, I did
$$ T=0.9-0.86 = 0.04 $$
$$ \sigma p = \sqrt{\frac{0.9\cdot 0.1}{100} + \frac{0.86 \cdot 0.14}{100}} = 0.01450517149 $$
$$ t = \frac{0.04-0}{0.01450517149} = 2.757637166 $$
$$ t > z{0.025} = 1.96 $$
So I can accept with 95 percent confidence that the two rates are significantly different.
topaz sinewBOT
Can someone help me solve a doubt?
I have these two samples:
$$ Sample1: (OK=90,...
thorny flameBOT
alber848
neon iron
I then tried to come to the same conclusions using a Fisher exact test
Which lead to these results
Now, my p-value here is 0.5146 and would lead me to reject the hypothesis of the two rates being significantly different... is this normal??
Am I doing something wrong or is this huge difference due to the fact that I have very little sample sizes? (100 for each sample)
Can someone confirm me the fisher exact test p-value result essentially?
topaz sinewBOT
@neon iron Has your question been resolved?
neon iron
<@&286206848099549185>
topaz sinewBOT
@neon iron Has your question been resolved?
topaz sinewBOT
@neon iron Has your question been resolved?
topaz sinewBOT
@neon iron Has your question been resolved?
neon iron
<@&286206848099549185>
topaz sinewBOT
@neon iron Has your question been resolved?
neon iron
watch this to calm urself down <@456226577798135808>
Bruh
winter current
did u watch it?
neon iron
Yes
winter current
its so trolls
wooden matrix
neon iron
Still up
pulsar falcon
Can someone help me solve a doubt?
I have these two samples:
$$ Sample1: (OK=90,...
huh what is that formula you are using? Its wrong
neon iron
huh what is that formula you are using? Its wrong
🤔
What’s the correct one?
Are you sure it’s wrong? 🤔
I think it’s right
pulsar falcon
(300,800) (360,740)
those sum to 1100 and in text says n=1000
pulsar falcon
This is Chi squared test
no its not
neon iron
those sum to 1100 and in text says n=1000
(300,700), (360,640)
pulsar falcon
The prop.test test statistic is
so idk what you are complaining about
A chi-square test for equality of two proportions is exactly the same thing as a z-test.
neon iron
The prop.test test statistic is
That’s exactly what I used…..
neon iron
A chi-square test for equality of two proportions is exactly the same thing as a...
Also no
pulsar falcon
Yes it is
neon iron
Using prop.test:
Anyways, this is wrong
pulsar falcon
no its not
neon iron
Using fishers test:
This is right
neon iron
no its not
Yes it is
pulsar falcon
?
How exactly do you think its wrong? Clearly the difference between an exact test and z-test should not be that different (100 is also a big size)
If that was the case clearly theory is broken
neon iron
I have it right here straight from the slides
neon iron
Using prop.test:
This is a chi squared test which yield different results from the normal test but similar result to the fisher test
pulsar falcon
And I suggest you try googling before claiming false stuff like this
no
neon iron
And indeed you got different results from the normal test
And similar results to the fisher test
neon iron
I have it right here straight from the slides
Bro sorry I’m gonna trust my professor with over 40 years of experience in the field over you….
neon iron
The prop.test test statistic is
Do the same using this formula
You will see that the results aren’t the same from what you sent
pulsar falcon
**alber848**
,w sqrt((0.9)*0.1/100+(0.86)*0.14/100)
thorny flameBOT
pulsar falcon
the problem is you can't calculate
and I am right which you would also see if you googled
and that R is build by a lot of stat people, so trusting R over professor should actually be better
(and am studying stats myself and have been a TA in several stat courses in my uni)
pulsar falcon
0.04...=0.01... in your mind?
neon iron
.close
topaz sinewBOT
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Available help channel!
north needle
topaz sinewBOT
north needle
chilly kestrel
uwu rotate
thorny flameBOT
chilly kestrel
np
north needle
could you spot what im doing wrong here? I cant find why its wrong
chilly kestrel
you want to simply [ \left(1+\frac x8\right)^{-\frac12} ?]
thorny flameBOT
Lance
north needle
yeah through binomial expansion
as in through the (1+x)^n equation
the second section is supposed to be
but i keep getting 5x^2 no matter what
chilly kestrel
where does the 1.2 come from again?
chilly kestrel
\[ 1 \cdot 2 \ne 1.2 \]
Lance
chilly kestrel
;-;
chilly kestrel
LOL
north needle
ill have to make a note of this
thanks lol
this is honestly ridiculous
.closoe
.close
wispy portal
stochastic calc question (Ito integral) - how does one compute: dW^4(t) - is this just the 4th derivate of W(t) using F(t,W(t)) in the ito-doeblin formula?
topaz sinewBOT
stochastic calc question (Ito integral) - how does one compute: dW^4(t) - is th...
@wispy portal Has your question been resolved?
wispy portal
<@&286206848099549185>
wispy portal
hmm - no love for stochastic calc? everyone on spring break? 🙂
I think am just confused by the notation... dW^4(t) is this the same as d( W(t)^4 ) ? so really its the derivative of the function W(t)^4 ?
<@&286206848099549185> ?
sweet shard
stochastic calc question (Ito integral) - how does one compute: dW^4(t) - is th...
Probably should post in #advanced-probability
topaz sinewBOT
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neon iron
Hello all, I apologize if this question has an obvious answer but I’d like to sure. Regarding discrete math, are contrapositive and contraposition the same thing?
topaz sinewBOT
Hello all, I apologize if this question has an obvious answer but I’d like to su...
@neon iron Has your question been resolved?
topaz sinewBOT
@neon iron Has your question been resolved?
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hidden ridge
topaz sinewBOT
hidden ridge
tried brute force and got:
best ans is a = 4, b = 4, u = 4, ans = 112.
any non-brute force way?
topaz sinewBOT
@hidden ridge Has your question been resolved?
topaz sinewBOT
@hidden ridge Has your question been resolved?
topaz sinewBOT
@hidden ridge Has your question been resolved?
vale jacinth
any non-brute force way?
At least I can make that list shorter
That expression is symmetric we can just assume that u<=a<=b
vale jacinth
Got it. That sum equals 72+uab-(u^2+a^2+b^2)/2
Now notice that if u,a,b are not equal, so (4,4,4), then there must be two of them whose differences has absolute value greater than 1
so when (u,a,b) doesn’t equal (4,4,4) then say u-a>=2, then uab can be greater: (u-1)a(b+1)
Similarly u^2+a^2+b^2 can be smaller, (u-1)^2+(a+1)^2+b^2=u^2+a^2+b^2+2(1+a-u)<u^2+a^2+b^2
So uab is greatest and u^2+a^2+b^2 is smallest iff u=a=b=4
vale jacinth
Got it. That sum equals 72+uab-(u^2+a^2+b^2)/2
This is because 144= (u+a+b)^2=u^2+a^2+b^2+2(ua+ab+ub)
topaz sinewBOT
@hidden ridge Has your question been resolved?
topaz sinewBOT
@hidden ridge Has your question been resolved?
sage sedge
That expression is symmetric we can just assume that u<=a<=b
hm the symmetry gave me an idea for an easier way
@hidden ridge have you learned about the AM-GM inequality?
(if you still need help)
sage sedge
<@!782087086416461855> have you learned about the AM-GM inequality?
(essentially that the geometric mean of some numbers is at most equal to their arithmetic mean)
sage sedge
(essentially that the geometric mean of some numbers is at most equal to their a...
here, the three “numbers” are (u+1), (a+1), and (b+1)
another nice fact is that the geometric mean equals the arithmetic mean when all of the numbers are the same
so here, it would be when u+1=a+1=b+1
and that would mean they’re all 5 in this case
so u=a=b=4 which is what you found
vale jacinth
Now notice that if u,a,b are not equal, so (4,4,4), then there must be two of th...
Just use this
But seems he didn’t read it or he doesn’t want to
vale jacinth
It doesn’t help you if you refuse to take a look at what people answered you right.
If x+y=k then xy=x(k-x) are maximum when x=k/2, so when (u,a,b) doesn’t equal (4,4,4), then there exists two of them whose difference is greater than or equal to 2, for example u-a>=2, then uab<(u-1)(a+1)b
and u^2+a^2+b^2>(u-1)^2+(a+1)^2+b^2 this case
So if (u,a,b) doesn’t equal (4,,4,4), uab could be bigger and u^2+a^2+b^2 could be smaller
And that sum you are looking for =72+uab-(u^2+a^2+b^2)/2
You understand the fact I used? That (u,a,b) doesn’t equal (4,4,4) then there always exists two of them whose difference is greater than or equal to 2? Because you can’t find s such that s+s+(s+1)=3s+1=12 or s-1+s+s=3s-1=12. So you can’t find (u,a,b) such that the maximum of their differences is 1, it’s either 0 or greater than 1
sage sedge
It doesn’t help you if you refuse to take a look at what people answered you rig...
i think this is close to one of the lemmas used in proving the AM-GM inequality actually
sage sedge
But seems he didn’t read it or he doesn’t want to
sorry 😅 i thought i would offer a different solution that was less from-scratch. i get kinda freaked out when i see a whole bunch of expressions and reasoning
frozen perch
well, there are various ways to prove AM-GM
i learned cogwheels' method as a sturm-type method, and that's indeed one of the ways to prove AM-GM
vale jacinth
He is just weird. He ignored me last time too. He just won’t take a look, and doesn’t ask back if anything I said he doesn’t understand. Last time he asked a number theory question, Mat confirmed my thought and we worked out the solution he ignored that too
That only 2,4,8,2p doesn’t divide A(m) thing
mortal thunder
(essentially that the geometric mean of some numbers is at most equal to their a...
@hidden ridge mousie 
mortal thunder
sorry 😅 i thought i would offer a different solution that was less from-scratch...
wdym "less from scratch"... if that's the case then one should always prove the AM > GM > HM, Jensen's, cauchy, and all before applying it!?
You saw non-negative, and you did the right thing... it was a totally different scenario if your equality holding gave you non-integer solutions for u, a, b but that doesn't seem to be the case here
so be confident smh
sage sedge
woops i think i read cogwheel’s comment wrong
thought they were talking about me not reading their work
sage sedge
so be confident smh
thanks lmao
topaz sinewBOT
@hidden ridge Has your question been resolved?
sweet shard
.close
topaz sinewBOT
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remote grotto
how do i solve this?
topaz sinewBOT
how do i solve this?
keen venture
W = ∫ F dx
topaz sinewBOT
@remote grotto Has your question been resolved?
gilded raven
topaz sinewBOT
torpid matrix
Theres infinite solutions, not a great question
do you want one solution or you want a way to represent all of them?
gilded raven
One solution
gilded raven
do you want one solution or you want a way to represent all of them?
One solution
If I made the weight of herb 1 x and weight of herb 2 y
torpid matrix
okay pick any number of kilos of herb 1, find the price of that, find out how much more the mixture is, then find out how many kilos of herb2 that is
gilded raven
And made them equal so it’ll be 1.8x = 1.6y
And made an equation for the mixture where its 56 = 1.8x + 1.6y
Then solved simultaneously
Would that worK?
@torpid matrix
Sorry I had an exam and I question similar to this came up and now im paranoid if I did it correctly or if I messed up
torpid matrix
1.8x + 1.6y = 56 is the price formula, the number of kilos would be (x+y) for any (x,y) solution to that
so if you got that, then yes
gilded raven
1.8x + 1.6y = 56 is the price formula, the number of kilos would be (x+y) for an...
But the part were I made 1.8x = 1.6y is that right?
torpid matrix
if 1.8x = 1.6y that would imply the final mixture is half herb 1 and half herb 2 by price
1.8x is the price of x kilos of herb 1, and 1.6y is the price of y kilos of herb 2
so by setting them equal to each other the prices of the herbs have to be the same
gilded raven
so by setting them equal to each other the prices of the herbs have to be the sa...
Ah k so that’d be wrong right
torpid matrix
if thats how the problem was written, then yes
that constraint gives you a solution but it doesnt give you all of them
gilded raven
that constraint gives you *a* solution but it doesnt give you all of them
By a solution you mean a weight for herb 1 and herb 2 correct?
torpid matrix
yes
gilded raven
yes
So if you were to find all the solutions, there would be multiple masses of herb 1 and herb 2 could be right which can satisfy the mixture solution
torpid matrix
yes
gilded raven
yes
If I worded the question like “If herb 1 is sold at 3.8 dollars per kilo and herb 2 is sold at 2.5 dollars per kilo, and their mixture is sold 2.8 dollars per kilo, what mass if each was present in the mixture?”
Would that make a difference to the solution
Or would there still be multiple
torpid matrix
that would not be possible, because thats more expensive than either of them
gilded raven
that would not be possible, because thats more expensive than either of them
Sorry how about now
topaz sinewBOT
@gilded raven Has your question been resolved?
elfin spruce
Help
neon iron
Split the force at an angle into components
elfin spruce
Is it the U and R?
elfin spruce
Ok it 8.91R+12.54U
neon iron
Now add them into a single vector
elfin spruce
15.38?
neon iron
And the angle?
elfin spruce
It 83.54?
elfin spruce
But idk
neon iron
To get the angle take the arctan of the quotient of your vector components
elfin spruce
I dont the words
elfin spruce
54.6?
neon iron
Yes
neon iron
Ok it 8.91R+12.54U
Also, when calculating these use more decimal places to avoid rounding errors
elfin spruce
???
neon iron
?
neon iron
How did you get 83.54 degrees?
???
elfin spruce
Idk im confused
neon iron
Ok
Let’s start from the beginning
Split the force at an angle into components
Using sin and cos
- Add the upwards vector
- Use tan-1 to find the angle of the resultant vector
- Use Pythagoras theorem to find the magnitude of the resultant vector
elfin spruce
- 8.91R +12.54U
- 54.6
- 15.3831
neon iron
2. 8.91R +12.54U
3. 54.6
4. 15.3831
Add more sig figs in step 1 and 2 because you are subbing values back into trig functions
And add units
elfin spruce
Idk the unites it is not given
neon iron
The units of the angle is given
elfin spruce
The circle thing?
elfin spruce
So it 54.9。 and 15
neon iron
Yeah
elfin spruce
So is right?
patent flax
Prove, for the given set L=[0,1,....,n] for any given number n which is an integer that lies in the interval [0,∞), that, if all values of 2^L[i] for all integral values of i=0,1,…,n, where L[i] denotes the ith term of the list L, was to be made into a list M, then there will always be a unique expression of the sum of some terms in M that will equal to any given integer between the interval [1,2^(n+1)-1].
topaz sinewBOT
Prove, for the given set L=[0,1,....,n] for any given number n which is an integ...
patent flax
and no this is not homework
becoz I'm only in 7th grade
now I know most of you will think it's not normal for a 7th grade to be doing this
but it ain't normal for G7 to do this is it
and if you can
what's the problem with this proof
ah nvm
you guys would tell me eto be older anyway
.close
patent flax
exercise huh
lemme see
BO=OX then BOX is isosceles
if 5 = 6 then EOX is also isosceles
well the others IDK
neon iron
For the following, I need to find: No solutions, a unique solution and or many solutions. I have turned the above into an augmented matrix and reduced it using REF to:
[3 k 2 ]
[0 (-3-k/3) -3h-2/3]
Not sure what I do from here
topaz sinewBOT
For the following, I need to find: No solutions, a unique solution and or many s...
alpine mist
So, an augmented matrix has 1 solution if it can be reduced to the identity with any vector in the right most column, it has no solutions if it has a row of zeros with a non-zero term in the right most column, and infinite solutions if it has a zero row
one solutions
$\begin{bmatrix}1&0&a\ 0&1&b\end{bmatrix}$
no solution
$\begin{bmatrix}1&0&a\ 0&0&b\neq0\end{bmatrix}$
infinite solutions
$\begin{bmatrix}1&0&a\ 0&0&0\end{bmatrix}$
neon iron
epic latex fail lol
alpine mist
omg
alpine mist
I'll just leave now
thorny flameBOT
Zybikron
neon iron
alpine mist
meh, i do math. English is questionable.
alpine mist
I hate you
solemn fiber
hello i need help with my homework. if you threw a rock straight up it would be h(t)=20t-4,9t^2.....t is seconds and h is height. the question is how fast is the rock after 1 sec and 3 sec. how high did the rock go. and how fast was it at h=10 m
topaz sinewBOT
hello i need help with my homework. if you threw a rock straight up it would be ...
neon iron
To get to Valhalla you need to take initiative! consider the deriative!
mellow venture
mellow venture
yes
mellow venture
thought it said what time was it at h=10
solemn fiber
ohh sorry i probably confused you
i have to find what speed the rock has at 1 and 3 seconds
neon iron
Brothers, lay down your weapons! for with the derivative you can calculate the maximum height in seconds !
solemn fiber
how high the rock got in total
mellow venture
Brother in Christ, don't listen to this heathen and cut down Odin's tree in order of the Bishop!
solemn fiber
and what speed it had at h=10m
neon iron
😬
solemn fiber
the height h in meters is the first line below
h(t)=20t-4,9t^2
t=seconds
h'(t) = speed
A) find the speed after 1,0 seconds and after 3,0 seconds
B) how high did the rock go
C) what was the speed of the rock at h=10 m
pliant wind
the height h in meters is the first line below
for C): We know that the only variable in h(t) is time. We also know that h(t) is distance, and the derivative of distance is velocity. So h'(t) is velocity (but in this case, we can just say it's speed). We know that the rock is at height=10 at some certain time. So if we set h(t) to 10 and solve for t, we'll know the value of t for when the rock is at height 10. If we know the time its at and we know what the function h'(t) looks like, then we can say: at the time t we found at height 10, if we use that time in h'(t), then h'(t) will be the speed of the rock at that time. Since that's the time when height=10, we thus know that the speed of the rock at h=10 is whatever we find for h'(t) when we plug in the value we find for t into h'(t)
**for A): ** We know that h'(t) is speed. We have h(t): our original function. Since h'(t) is the derivative of h(t), we find h'(t) by taking the derivative of h(t). Then, the speed after 1.0 seconds is when we plug t=1 seconds into our h'(t) speed function, since if we do that we'll find the speed (which is h'(t) ) at time=1 seconds. We do the same thing for t=3 seconds. There will be two answers since there's a speed for t=1 seconds and a speed for t=3 seconds
**for B): ** I'm guessing the question is referring to time=1 seconds and time=3 seconds when it asks "how high did it go". We have a function for height: it's h(t) ! So if we plug in time = 1 seconds into h(t), we'll find the height of the rock when time=1 seconds. Similarly, if we plug in time=3 seconds into h(t), we'll find the height of the rock when time=3 seconds.
solemn fiber
can you give me the anwser to 3 seconds on A just so that i know i understood my method
i solved for 1 sec but im not sure if its right
like could you show how you would solve 3 sec
pliant wind
is $h(t)=20t-4 + 9{t^2}$
thorny flameBOT
quevorak
pliant wind
i was just a little confused by what h(t) was bc you wrote it with a comma (h(t)=20t-4,9t^2). wanna make sure i'm using the right equation
solemn fiber
yes thats correct
thorny flameBOT
quevorak
pliant wind
glad it helped
solemn fiber
but like i got the answer h=5.3
is that the speed?
or is that the height
im guessing the height
gleaming mica
solemn fiber
but now to find the speed at 3 seconds i have to do what exactly?
sorry for being dumb asf btw lmao
pliant wind
find h'(t) when t = 3 since h'(t) is our function for speed
viscid thistle
hello i need help with my homework. if you threw a rock straight up it would be ...
find h’(t) my guy and sub those values in. and how did the rock go is the max point. find x where h’(x) =0 and sub that x in h(x)
h’(t) is the differential of h(t) with respect to t
solemn fiber
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solemn fiber
wait sorry boys
how high did the rock go?
please give me the answer, then i can go through it and find out how you guys did it
thats the best way i learn
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naive glacier
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https://i.imgur.com/Mo0OmZj.png
naive glacier
Can someone check my answer?
I have the for loops from i=1 to i=n equaling 2n
because for loops is C=2
and runs n times
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neon iron
a) At the local ice rink, popcorn is sold in a square-based pyramid-shaped container with side lengths of 15 cm and a height of 21 cm. Calculate how much popcorn this container will hold.
b) After a hockey game at the local arena, a tired player gets a drink from the water cooler. The water cups provided have a conical shape with a diameter of 11 cm and a height of 12cm. How much water will fit into this cup?
c) A basketball has a diameter of 24.8 cm. How much air does it take to fill this basketball?
d) During the holiday season, a company packages their chocolates in a box shaped like a pyramid. The base of the box is a square with side lengths of 10 cm. The pyramid is 12 cm high. Calculate the amount of packaging needed for this pyramid-shaped box.
e) A new popsicle on the market has the shape of a cone with a radius of 1.5 cm and a height of 15 cm. Calculate the surface area of this popsicle so that the company will know at least how much packaging may be necessary.
f) A chocolate in the shape of a sphere is packaged by wrapping it in colored foil. If the chocolate has a radius of 1.8 cm, calculate the amount of foil needed to package the candy. Draw a diagram.
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a) At the local ice rink, popcorn is sold in a square-based pyramid-shaped conta...
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neon iron
At the local ice rink, popcorn is sold in a square-based pyramid-shaped container with side lengths of 15 cm and a height of 21 cm. Calculate how much popcorn this container will hold.\
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sick mulch
In the figure below AM is three times longer than MD. CD is 10cm. How to find AB? 🤔
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In the figure below AM is three times longer than MD. CD is 10cm. How to find AB...
sick mulch
maiden igloo
you can prove that MCD and AMB are similar triangles
sick mulch
How would you prove it?
kind axle
How would you prove it?
They have the same angles
wary oak
@sick mulch Because both triangles are right triangles, you only need to prove that two angles of them match
sick mulch
I was first thinking of Pythagoras, but that did't work out
Angle A and D is 90
M is on the A and D line, that means they are equal?
wary oak
yeah the angle at M is the same for both triangles
sick mulch
What is the reason for that? Cuz, they are on the same line?
wary oak
If two lines intersect they form 2 pairs of opposite angles
sick mulch
vertical angles are congruent?
So when I have proved that the same triangles, I can then just multiply by the ratio. This means that AB = 10cm * 3? So when I have proved that the same triangles, I can then just multiply by the ratio. This means that AB = 10cm * 3? 🤔
wary oak
yes
frank bramble
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frank bramble
Find the horizontal and vertical shift
amplitude
frequency
and period
don't rly know where to start
<@&286206848099549185>
SOMEONE PLEASE HELP
.close no one is helping
spiral briar
I need help
topaz sinewBOT
I need help
neon iron
in my video game I have 8 different boxes, out of the 8, there are 3 boxes that contain special things what I want.
If I can choose 5 at random, what is the chances that I 2 that I want?
And the chnance that I get all 3 that I wanted?
neon iron
There is no double getting, so chance to get what I want is 3/8,
Then to get my next box the chance of that is 2/7 ?
Then to get the last box is 1/6?
But I get 5 chances so maybe it's like
I'm stuck because like, if I don't get the box on one try then it's like
3/8 * 3/7
but if i do get the box it's like 3/8 * 2/7
so how does it work I have to construct like a few different probability trees then add it together or something
chilly kestrel
in my video game I have 8 different boxes, out of the 8, there are 3 boxes th...
hint: if i have exactly 2 special boxes, then how many ways are there to 'choose' these 2 special boxes out of 3? and how many ways are there to 'choose' the 3 non-special boxes out of the 5?
chilly kestrel
so how does it work I have to construct like a few different probability trees t...
if it's for a videogame, you can always run a quick simulation, should be easy enough to program :)
neon iron
hint: if i have exactly 2 special boxes, then how many ways are there to 'choose...
is it: 3 choose 2, meaning 3 different ways?
neon iron
3 choose 1
chilly kestrel
ok so how many ways are there total that let us pick 2 special boxes?
neon iron
ok so how many ways are there total that let us pick 2 special boxes?
i forget how to do it the short cut way but in writing way you have to tally it like:
yes, yes, no, no, no
yes, no, yes, no, no
yes, no, no, yes, no
like that for all the total ways of getting my 2 special boxes in my 5 tries
chilly kestrel
no i mean
neon iron
if it's for a videogame, you can always run a quick simulation, should be easy e...
oh its not my video game, it's a video game im playing and i wanted to know what's my chances of winning xD
chilly kestrel
ah lmao
how many ways are there total that let us pick 2 special boxes out of our drawn 5
you've already calculated the number of ways to rearrange the special and non-special boxes
neon iron
how many ways are there total that let us pick 2 special boxes out of our drawn ...
i guess 5 choose 2?
chilly kestrel
ok i'm still not clear enough i guess :(
how many ways of choosing 5 out of 8 boxes are there that suffice your question?
neon iron
im not smart enough i forgot
chilly kestrel
notice that such a choice has a unique choice of having selected 2 special boxes and 3 non-special boxes
neon iron
ya
neon iron
8 choose 2 * 8 choose 3
like that for how many different ways we can have a combination of total 5 boxes where 2 is the specail one and 3 is a normal one
28 * 56 = 1568
neon iron
oh ya that makes sense
3 * 10 = 30
and then the number of ways to choose 5 boxes is 8 choose 5
chilly kestrel
yup
chilly kestrel
you got it
chilly kestrel
do you think you can do the 3 special box case now?
neon iron
i think so
there is only 1 way to get all 3 boxes (3 choose 3)
and then there is 5 non-special boxes and you choose 2 ( 5 choose 2)
for a total of 5 boxes chosen
and that's 1 * 10 = 10
and out of the 5 boxes chosen from the 8 (8 choose 5 = 56)
so the probability to get all 3 special boxes is 10/56
which is 17.8%
chilly kestrel
yup! now please stand by for me to write a simple program for this :)
neon iron
okay
chilly kestrel
import random
trials = 10 ** 6
successes = 0
for i in range(trials):
choice = random.sample(range(8), 5)
successes += sum(box < 3 for box in choice) == 2
print(successes / trials)
0.534463
so for a million trials (at this point just loop through all possible samples lol) the probability seems to be roughly 0.534463 to get exactly 2 special boxes
neon iron
yay okay
chilly kestrel
and the probability to get at least 2 is 0.714414
(the expected probability was 0.714286)
so we've probably done everything correctly
chilly kestrel
comb(inatorics) is always a bit of fiddling :(
neon iron
i will close now so other people can get help too
chilly kestrel
alright
kindred kernel
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bright panther
,rotate
thorny flameBOT
kindred kernel
I can't figure it out
bright panther
ok
kindred kernel
what are you stuck on
All
kindred kernel
Nah
bright panther
honestly
imo its hard to explain without being there
hard to explain with words
also bcs im a shit explainer
kindred kernel
hard to explain with words
Do you know the answer
bright panther
i would say B F E too...
kindred kernel
Hmm
sweet shard
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• After 15 minutes, feel free to ping @Helpers.
light oyster
okay
if a cuboid of weight 100n has sides 5 cm by 10cm calculate the pressure extended when it lies on the side
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neon iron
I am genuinely confused- for the first screenshot, I could solve it because there was a number with the x that I can divide with- but in the second question I can’t do the same and I’m just there stuck with the question they give me
topaz sinewBOT
I am genuinely confused- for the first screenshot, I could solve it because ther...
neon iron
So my question that I’d like to ask is what can I do to solve this- when there’s nothing to divide like the prev question?))
neon iron
Oh huh :00 I’ll I’ll try and see how it goes- thank you !
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grand wing
When integrating using horizontal strips, we were taught that to get the area it is right function-left function. What is the right function in this case? The blue or the green line?
topaz sinewBOT
When integrating using horizontal strips, we were taught that to get the area it...
grand wing
In this graph, it is quite obvious that the right function is the red line (quadratic)
modern bloom
When integrating using horizontal strips, we were taught that to get the area it...
There are two right functions, which means that you have to separate the region into 2 regions
modern bloom
In this graph, it is quite obvious that the `right function` is the red line (qu...
Yes, the red one is the right function, but there are 2 left functions
grand wing
separate into two regions... hmm how do i that..?
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lavish musk
separate into two regions... hmm how do i that..?
The region can be separated as 0 < y < 5 and -1 < y < 0. Notice how the right curve is different on these two intervals. Find the equation for the right curve on each of these intervals.
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tough current
how would i go about calculating RTP(return to player) of a slot machine. My slot machine has 7 icons, they all have same probability of happening, 1/7. The slot machine is only 1 row, 3 columns
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how would i go about calculating RTP(return to player) of a slot machine. My slo...
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fickle elbow
int sqrt(a^2 - x^2) dx
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int sqrt(a^2 - x^2) dx
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neon iron
Hi I am grade 7 and always have problems with metric unit and I forgot it completely I would really appreciate if I get to learn these
- general overview
2)express ( metric unit) to another metric unit - how to do the working
topaz sinewBOT
Hi I am grade 7 and always have problems with metric unit and I forgot it comple...
olive plume
count how many zero are there
neon iron
km is 1000, cm is 100, mm is 10, so its six zeros
Ohhh
So let’s say
We have to change
38 km to cm
We multiply by 5 zeros?
I found this "https://www.youtube.com/watch?v=WL6_HKyipHk"
If you are native arabic, this may be more helpful. "https://www.youtube.com/watch?v=f3cSMx0o8zQ"
neon iron
True
Ohhh
Okay we have also have fr
*ft
And uh
Wait let me try to name it
Inch Cm mm meter Kilometer
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steep tiger
inch isn't metric
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olive plume
Inch Cm mm meter Kilometer
inch is non metric while cm, mm, m, km are metrics
neon iron
Ohhh
olive plume
so you will have to convert non metric to metric or metric to non metric first
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neon iron
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neon iron
I had to do 5b and 5d, do these proofs make sense?
Idk if this is academic dishonesty since I did it myself
sweet shard
this is correct, but you have to re-write the proof backwards starting with
Let $\eps > 0.$ Define $k = ... $ and basically do the work in reverse
thorny flameBOT
riemann
sweet shard
You want to conclude that the difference in absolute values is less than epsilon
Read the "proof" here
https://www.milefoot.com/math/calculus/limits/DeltaEpsilonProofs03.htm
neon iron
ok
is the proof I wrote still valid though?
I know the result is correct, but does the proof hold
sweet shard
Read the "proof" here
https://www.milefoot.com/math/calculus/limits/DeltaEpsilo...
write it in this style and share it
sweet shard
Let $\eps > 0.$ Define $k = ... $ and basically do the work in reverse
this should be your first line
neon iron
read #❓how-to-get-help
forest oak
Please type the equation for ans no 2,5&10 Exercise 3.2
neon iron
read #❓how-to-get-help
you're just barging in and asking we stop what we are doing to help you, it's rude
forest oak
How may I define my problem?
pulsar wyvern
How may I define my problem?
This channel is currently being used. Please ask in one of the avaiable help channels. Thank you.
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shadow holly
Does the first part (a) look right to anyone? I think I fixed it now. Thanks!
sweet shard
Yea
shadow holly
Thank you! Also, last question - does c) make sense to you? I’m unsure about the answer but I kinda just bs’ed it and hoped it’d work
worthy storm
Thank you! Also, last question - does c) make sense to you? I’m unsure about the...
you didn't say why equality of the null space dimension implies the same rank. this need not be true for general matrices; what reasoning are you using to conclude that it's true here?
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shadow holly
you didn't say why equality of the null space dimension implies the same rank. t...
Honestly.. no reasoning at all which is bad. Should I take a look at the rank-nullity theorem and try to pick out something from there?
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gloomy moon
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warped thistle
Define all the terms in terms of cos x & sin x.. like csc x =1/sin x & tan x =sin x/cos x
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native arch
Hello, I’ve solved for a, but how do i solve for b?
topaz sinewBOT
Hello, I’ve solved for a, but how do i solve for b?
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native arch
a
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static void
is there a problem you need help with or are you here to mess around?
is there a screenshot of the original problem?
you could post?
fossil widget
good one man
vapid lichen
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late crypt
hi
elfin basalt
from the first equation, you subtract y
then you get x=xy-y
and then you can group the right side of the equation to make it simpler, each element has y, so you can write it as y(x-1)
you "isolate" y, and then multiply it with the other elements
does it make sense?
late crypt
then you get x=xy-y
why xy-y
late crypt
ok
low edge
How to solve this question?
topaz sinewBOT
How to solve this question?
olive plume
tangent 45 = opposite/10
tan (45+15) = (x+opposite)/10
and tangent 45 is actually = sqrt(3)
low edge
sorry im still not sure what to do from there
olive plume
tangent 45 = opposite/10
opposite = 10 tan 45
opposite = 10
tan (45+15) = (x+opposite)/10
x + opposite = 10 tan 60
x + 10 = 10 tan 60
x = 10 tan 60 - 10
since tan 45 = sqrt(3)
x = 10 sqrt(3) - 10
x = 10(sqrt(3)-1)
broken trout
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broken trout
how do u do part c
gleaming thunder
use 2*theta/2 = theta to link back to cos theta. Then either you know the half-angle formula or you prove it using the double angle formula and the pythagorean identity to express cos theta = cos(2*theta/2) in a way that can be solved for cos(theta/2)
hexed hornet
your question makes no sense
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quasi bison
Hi can someone please tell me what I did wrong at 3h the answer is (x+4.5)^2 - 22.25 how did they get -22.25 I got -42.25
topaz sinewBOT
Hi can someone please tell me what I did wrong at 3h the answer is (x+4.5)^2 - 2...
quasi bison
Oh okay thanks! because I went through multiple of these questions and I basically copy pasted the formula but for some reason the book said i was wrong! But thanks for the confirmation have a good day bye!
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alpine mist
mostly makes sense. Could use some sentences.
I also don't know why you indexed your alphas in M?
inner bridge
Ok thanks
inner bridge
Oh yeah i did that to show it's a square matrix of size n but i guess it could suggest that the alphas are of different values so I will change that
alpine mist
Oh yeah i did that to show it's a square matrix of size n but i guess it could s...
just write out that M has whatever dimensions. Use sentences.
vital relic
Even so, I'm not so sure about that assertion
that M is matrix aI
You should justify why this is necessarily the case.
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worldly musk
Is the convergence interval for my series all real numbers?
topaz sinewBOT
Is the convergence interval for my series all real numbers?
worldly musk
I have been trying to work it out for some time now, this is the maclaurin series (i hope at least) for e^(-x^2)
I did the ratio test and got lim k->infinity (-x^2)/(k+1)
my question is, does this allow x to be anything?
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teal glacier
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glacial kite
How would you decode encrypted ciphertext without the key "K" or the decoded message "p". Like all I have is the encrypted message "c" that needs to be used to figure out the key to decrypt them
topaz sinewBOT
How would you decode encrypted ciphertext without the key "K" or the decoded mes...
shrewd horizon
i'm guessing you'd probably have to use the fact that the plaintext is actual readable text and not just nonsense
shrewd horizon
no, i mean the plaintext
glacial kite
I don't have that as far as I know
shrewd horizon
i know that
glacial kite
oh alright go on, sorry
shrewd horizon
but you're trying to get it
glacial kite
right
shrewd horizon
if you end up getting plaintext that clearly doesn't make any sense, then you've probably got the wrong key
glacial kite
ye
shrewd horizon
this does look potentially a bit difficult because it doesn't look like there's a straightforward way to do simple frequency analysis ("this letter is the most common so it's probably e"), but if they're asking you to do this then there are probably enough patterns in plaintext to find the same patterns in the ciphertext and then use that to work out what's going on
glacial kite
So what should some of my first steps be, like I'm just not sure how to start looking as you described it
shrewd horizon
how big are the ciphertexts that they've given you?
glacial kite
really big
I can just provide a line
and the other thing though with what you said isn't the encrypted text going to be multiplied by the inverse of the key anyway, like would determining a frequent letter in the key not always correspond to say e as you say.
shrewd horizon
hmmmm
based on the description i think the same pair in the plaintext should be mapped to the same pair in the ciphertext
so if you can find common pairs that might be useful
long stirrup
based on the description, the method is given
you're supposed to be able to c×Kinv mod 27 and it will instantly work
shrewd horizon
we don't have K
glacial kite
finding common pairs of letters the same as pairs in the encrypted text you mean?
long stirrup
yes sorry
shrewd horizon
finding common pairs of letters the same as pairs in the encrypted text you mean...
well if the plaintext is ABCDAB, that should be mapped to something like XYZWXY - the same pair was mapped to the same thing
so if we find pairs that are common in the encrypted text, that tells us that they were also common in the plaintext
glacial kite
How would you know it should be mapped to something like that?, or is that just a random example
shrewd horizon
well it's not going to be those exact letters, but that structure
AB always maps to the same thing
glacial kite
right
so like while looking for pairs in the encrypted text what would I do with them?, like if I just took a small amount of the encrypted text
shrewd horizon
well presumably write down the frequencies
depending on how much text there is it might be easier (if you're allowed to do this) to just get a computer to count up the frequencies instead of doing it by hand, but either way: go through enough of the ciphertext to reasonably expect to see patterns, and look at which pairs are more common
glacial kite
its like ~2766 pairs of two letters