ah alright
#help-28
calm osprey
seems correct
pallid sentinel
x=20 and dx/dt=-5
calm osprey
nothing, god it's to late for me XD
pallid sentinel
I meant those are the stuff to plug in the equation lol
pallid sentinel
nothing, god it's to late for me XD
It's alright mate thank you so much for the help
have a good sleep
calm osprey
have a good sleep
thank you seems like i need it XD soory i couldn't be of more help
pallid sentinel
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hybrid sinew
hybrid sinew
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elfin elbow
if faced with a proposition that requires the proof by contradiction method to prove , after assuming it's negation is true , what's the thought process about finding and working my way to the contradiction ? like how to get the thought of it ?
thick dove
dull void
dull void
if faced with a proposition that requires the proof by contradiction method to p...
can you clarify what you are asking for a bit more
proof by contradiction is a very broad technique
because once you find any contradiction given your assumption, it is a valid proof
ivory cairn
if faced with a proposition that requires the proof by contradiction method to p...
generally just work towards something that can't be true.
Like, if you want to prove "If x and y are even integers, then x+y is even"
By contradiction, assume x and y are even and x+y is odd.
Then x = 2n, y=2m for some n,m integers, and x+y = 2k+1 for some k integer.
But that means 2n + 2m = 2k+1
and 2n+2m - 2k = 2(n+m-k) = 1
But 1 is not a multiple of 2, so contradiction.
^^ also this isn't the only contradiction you can come up with. There are several.
elfin elbow
i think this statement is particularly easy (although i may not be able to think about working the equations like that ... factoring and stuff) , reading harder proofs sometimes i see that getting to a contradiction seems accidental , like how did he even know what to do to get to the contradiction ?
how can i for ex prove that " if a is divisible by b then a^2 is divisble by b , for any a and b " is wrong by contradict
to what contradiction should i go
ivory cairn
prove it's wrong? or prove the contradiction is wrong?
elfin elbow
prove the statement is wrong using the same method (contradiction)
ivory cairn
well... that statement is true.
elfin elbow
hold on
sorry it's inverted
if (a^2 is divisble by b , then a is divisible)
by b
we can take for ex a is 4 and b is 8
then it's wrong
ivory cairn
how can i for ex prove that " if a is divisible by b then a^2 is divisble by b ,...
to prove it's true by contradiction:
Assume b divides a and b does not divide a^2.
b does not divide a^2 isn't great to work with. But you should have a definition for b divides. So start there and try to contradict something that's known (like getting 1=0 contradicts equality) or that contradicts your assumptions (like getting b divides a^2)
ivory cairn
we can take for ex a is 4 and b is 8
great, you just proved its wrong.
It's called a counter example.
elfin elbow
great, you just proved its wrong.
It's called a counter example.
yes i just want to prove it by contradict
so obviously i won't get 1=0 and i won't get that for most of the propositions i'm given to prove
also i don't understand why didn't we assume b does not divide a^2 because that's the negation of this implication and not "b divides a and b doesn't divide a^2" because that'll keep it true
ivory cairn
yes i just want to prove it by contradict
to prove a statement is false, the typical approach is to find a counter example. You did that.
ivory cairn
also i don't understand why didn't we assume b does not divide a^2 because that'...
that statement isn't true
ivory cairn
the negation of "P implies Q" is "P and not Q"
"b divides a and b doesn't divide a^2" this isn't true.
ivory cairn
just to be clear. Proof by Contradiction is not proving an implication is false. It is proving an implication (if P then Q) is true by showing it's negation (P and not Q) is false (i.e. leads to a contradiction when both P and not Q are assumed to be true)
If you want to prove an implication is false, just find a counter example.
elfin elbow
counter example is easier as you said but i want to practice contradiction of probs that require it
lemme rewrite the problem i'm facing :
for every a and b in R , a=b.k1 ====> a^2=b.k2
negation is :
there are values of a and b , for which a=b.k1 and a^2!=b.k2
so i have these two equations on either side of the implication and i don't know how to work them to a contradiction
i don't know if i should square , add , divide ...
ivory cairn
try something, see what happens.
elfin elbow
just to be clear. Proof by Contradiction is not proving an implication is false....
lol
i wasted your time trying to prove a false statement by proving it's negation is false
im gonna close
ivory cairn
🤷 it happens
check out the How to Prove It book. It'll have a chapter on contradictions with lots of examples and problems
A quick google found several universities have it free online.
elfin elbow
yeah chapter 3
i have it on a page right now i hope it doesn't require nothing but basic high school math and a decent english
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silver flower
It doesn’t, it’s just an abstract way to think about it
languid whale
Is it that
50% chance of 20
Where you get either 0 or 20
averages out to 10?
silver flower
Yeah “averages out” is alright, it’s not technically correct since the only two possibilities are 0 or 20 but it’s ok for the purposes of this video
languid whale
I see
Makes sense
Thanks!
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sly juniper
Hello guys how do i calculate the probability of hitting my desired parts based from the data i have
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sly juniper
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wild sleet
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final cedar
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final cedar
Does anyone know why this says the numerator can be used to determine vertical asymptotes?
velvet spoke
If the denominator had a zero there as well, you'd have 0/0 which could be a vertical asymptote
final cedar
no that would be a removable discontinuity; a hole
woven sand
Otherwise, usually the denominator is used to find VA's
final cedar
If anyone has the answer please ping me. this is on Khan Academy as well
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obtuse urchin
@torn joltnumber 8
You dont get thats a division of fractions?
idk if its correct but you have to do more
lemme show ya
simplification
wait
denominator is 5(x-3)
and numerator... well the root is negative
how would you
numerator stays the same denominator 5(x-3)
do you understand why?
because you need to simplify it as much as you can
i "translated" it
now you do ruffini with the numerator
do you know how?
find something inside the rectangle which in the end gives 0
but <@&286206848099549185> cuz i have to leave
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@sturdy flare Has your question been resolved?
sturdy flare
<@780712457903276043> Has your question been resolved?
Yes thank you
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tardy vapor
This is confusing me; what is theta here?
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This is confusing me; what is theta here?
rare dock
not sure if this is what you were asking, but $\theta_1 = (1,0,0,\ldots,0)$, $\theta_2 = (0,1,0,\ldots,0)$, etc.
glossy valveBOT
layla💜
rare dock
all k-tuples
tardy vapor
oh
tardy vapor
all k-tuples
then how do we get this later?
like how do we multiple a number and a tuple?
dull void
think of it as a vector
tardy vapor
think of it as a vector
uh okay
rare dock
it's probably component wise scalar multiplication and addition
dull void
the 0 probably implicitly means the 0 vector, unless the alpha thingy is also a vector and that is the dot product
idk man this looks like advanced book and maybe nonstandard notation
tardy vapor
the 0 probably implicitly means the 0 vector, unless the alpha thingy is also a ...
oh no its a number
dull void
then it must be zero vector
so just saying the ith component equals 0 there I am assuming
tardy vapor
are u sure its a tuple?
tardy vapor
This is confusing me; what is theta here?
they've defined the notation in the text
dull void
I've never seen notation like that except in reference to an ordered n-tuple
but if it is some weird notation only used in niche sub area of math I don't know
dull void
np
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ruby oak
Ive tries multiple times to work this out but I can't seem to. The question is:
Explain how to modify the graphs of f(x) and g(x) to graph the solution set to the following system of inequalities. How can the solution set be identified?
Y>x^2 -2
Y≥-x^2 +5
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Ive tries multiple times to work this out but I can't seem to. The question is:
...
@ruby oak Has your question been resolved?
ruby oak
<@&286206848099549185> pls
winged spire
<@&286206848099549185> pls
hello
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ruby oak
So can someone help me with this
ruby oak
Given the function f(x)=-4^x +5 and g(x)=x^3 + x^2 - 4x +5, what type of functions are f(x) and g(x)? Justify your answer. What key feature(s) do f(x) and g(x) have in common? Consider domain, range, x-intercepts and y intercepts
I'm going to ping again because I've been waiting over 2 hours. <@&286206848099549185>
brittle steeple
Tbh I think the helpers ping is a psyop
f(x) is exponential (a little less so with the +5 but still) and g(x) is polynomial
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ember tree
Does anybody know what I am doing wrong?
$10.36 an hour. What is the rate of increase on her salary.```
I am doing 10.36-9.25= 1.11/100 = 0.0111% as the increase rate?
but for some reason it says its 12%?
empty sapphire
so the rate of increase would be (new - old)/old to get a decimal. Then you multiply the that with 100 to get a percentage
you just forgot to divide by the old. Instead of the dividing by the old you divided by 100. So I think you just mixed up two ideas 🙂
ember tree
ahh okay, thanks 😄
empty sapphire
np!
ember tree
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vocal radish
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vocal radish
I don't know how to get the function for this problem
silk obsidian
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native briar
How do I manipulate e in this situation? I know how to do questions using polynomials/rationals using the formula but I'm unsure of how to solve this. I can't show work as I just don't know what to do with e. :/
sharp vine
find Q, then use slope formula
finding Q is about plugging given x into f(x)
for example
for x = -0.1
,w 10e^(1/2*(-0.1))
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native briar
Ah I see. And when it comes to f(x)-f(a) / x-a though I don't know how to manipulate Eulers. Should I look up laws or something? Could you point me in a direction as this is where I'm getting stuck:
native briar
I'm trying to calculate the slope of the tangent line using the derivative formula (I hope that's the right name)
sharp vine
aa, it's about b) ok
native briar
Yes yes 🙂
sharp vine
well
firstly I'd take out 10 as constant
then you'll stay with limit
$$\lim_{x \to 0} \frac{e^{0,5x}-1}{x}$$
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Modus
sharp vine
now let's substitute u = 0,5x
obviously if x -> 0 then u -> 0
limit becomes
$$2\lim_{u \to 0} \frac{e^{u}-1}{u}$$
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Modus
sharp vine
let's substitute
s = e^u - 1
u = ln(s+1) and s -> 0
it gives you
$$\lim_{s \to 0} \frac{s}{\ln (s+1)}=\lim_{s \to 0} \frac{1}{\frac{1}{s}\ln (1+s)}=$$
$$=\lim_{s \to 0} \frac{1}{\ln (s+1)^{\frac{1}{s}}}$$
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Modus
sharp vine
now I guess you see what we have here
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compact ore
hello
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compact ore
i need to write 1088 as power of 2
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i need to write 1088 as power of 2
compact ore
1088 as a power of 2
wet iron
you have a calculator?
compact ore
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placid storm
is this okay? idk what it means to include units
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is this okay? idk what it means to include units
shrewd hamlet
if its talking abt the rate of change of the number of bacteria, itd be bacteria/min
round harbor
please help
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weak maple
a) or b)
round harbor
both
weak maple
So you have 23.678, 6.72 and 65.08 kilometers.
round harbor
add?
weak maple
First round each of these numbers.
round harbor
ty g
weak maple
For b) you just add them without rounding.
elder lava
Help
cyan wedge
You need to distribute the negative sign
elder lava
To 4+2i?
cyan wedge
Yes
elder lava
cyan wedge
check the complex part, otherwise looks right (assuming it's subtraction)
it's not multiplication as I said before unless the subtraction sign is actually a negative sign
cyan wedge
oh
cyan wedge
The problem is 25/4+3i
yes, then your answer is correct
elder lava
Ah ok
cyan wedge
I was referring to this
cyan wedge
didn't distribute the negative properly
cyan wedge
yea thats right
elder lava
Ok and from there i distribute -4-2i to the parentheses?
elder lava
Oh no i was going to multiply
So when do u multiply
Bcz ik some problems ghats how u solve
Like this one
For example
cyan wedge
if it's like -(7+3i)(4+2i) then it's multiplication. If it's (7+3i)-(4+2i) that's subtraction. Put the negative sign in front, not in the middle. If you put it in the middle, that's bad notation.
cyan wedge
Or they just want you to subtract.
cyan wedge
Yea, subtract for the first one, multiply for the second one
cyan wedge
that's just addition? there's no + in the middle for B though.
cyan wedge
torn jolt
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torn jolt
Please explain me the equation 19.
its basically saying this:\begin{align*}u_{n+1}&=u_n+hv_n\u_{n+1}&=v_n+h(7-u_n)\end{align*} ie, read off each row of the vectors
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Toby
gloomy fulcrum
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tidal adder
Can anyone solve c?
gloomy fulcrum
you've interrupted my question -_-
but anyways, anyone know how I can go about solving this?
it's to do with circular motion
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Percy156
tidal adder
Anyone?
west delta
$r=\frac{v^2}{a_c}$
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Percy156
gloomy fulcrum
only g and not W?
west delta
Can anyone solve c?
power set is just all the possible subsets of that set right
tidal adder
Ikr
gloomy fulcrum
oh yh bc it's a and not F
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tidal adder
Can u pls help?
tidal adder
Yeah
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runic root
Hello, the problem is to find the zeros of a given polynomial and roughly sketch the graph of P(x). In this case the polynomial is x^4 -3x^2 -4 which I have factored down to (x^2 + 1)(x-2)(x+2). To sketch the graph I noted the zeros at x=2 and x=-2 and that the end behavior is the same as x^2, however when graphing the polynomial in desmos it looks more like a W as shown below. My question is, what effect does the term (x^2+1) have on the graph of a polynomial (and similar terms) and how can I predict this effect without the use of graphing tools, any help is appreciated
runic root
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torn jolt
Hello, the problem is to find the zeros of a given polynomial and roughly sketch...
Just an idea, but I think that whenever the exponents of the polynomial are only pairs, it will present this shape of an W in the graph, if the exponents are only odd, it will present a shape similar to an N
But I don’t have any explanation for why this happens
runic root
so you mean if there is a term of (x^even power + constant) it will add this feature to the graph?
torn jolt
so you mean if there is a term of (x^even power + constant) it will add this fea...
I guess so
runic root
ok well if true that is very helpful, I can do some checks pretty easily to find out
thanks
runic root
thanks 👍
empty sapphire
hi there! Did you try the hint? Like for example, what happens for f(2, 3)? What about f(3, 2)?
no I mean what do you get when you try those two values?
it produces a single number 🙂
yep!
lilac valve
Consider the two possibilities: that x>y, or y>x. See what the absolute value does in each case
empty sapphire
now try, say f(12, 2) and f(2, 12)
empty sapphire
I would double check that lol
lilac valve
Note how it always returns one of the original numbers
Yes, now what you have to do is prove it
Take it case-by-case. There are two possibilities: x>y, and y>x. For each possibility, try to simplify the expression by canceling out the absolute value
The expression in the absolute value is (x-y). If y is greater than x, what does the expression inside the absolute value look like after you apply the absolute value to it?
if x>y, then |x-y|=x-y, and if y>x, then |x-y|=y-x
So, you can simplify the expression for each of the individual cases x>y and y>x, yes?
so once you do that, it should be pretty obvious how you prove that this function returns the maximum value
Okay, for any case x>y:
f(x,y)=(x+y+|x-y|)/2
f(x,y)=(x+y+x-y)/2, because x-y is positive when x>y, so |x-y|=x-y
f(x,y)=2x/2, cancel out both y terms. y-y=0, and x+x=2x
f(x,y)=x, cancel out the 2s
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indigo aspen
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sand stone
have you learnt about geometric progressions
sand stone
what have you learnt
sand stone
so whats stopping you from applying it here?
sand stone
this is just a geometric sequence with sum to infinity is it not
hmm
try writing out the first three terms
of the sum
indigo aspen
of the sum?
indigo aspen
yep
sand stone
whats the starting term
sand stone
whats the common ratio
yep
so whats stopping you from plugging those into the
infinite sum formula
sand stone
no problem
indigo aspen
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still cove
How to know if your answer is part of the solution in exponential inequalities?
still cove
How to know if your answer is part of the solution in exponential inequalities?
Like how do I know what to use in my interval notation whether bracket or parenthesis
deft zodiac
do u mean ( vs [
still cove
do u mean ( vs [
Yes
still cove
Yeah but how do I know if that number is included or excluded
still cove
u can just plug it in to see if it fits
Like checking the answer?
deft zodiac
u literally plug it into the equation
like if weve
x>0
we can use
(0,inf)
then we can try
x=0
0=0
thus 0 is not >0
so its not included
still cove
Oh okay thanks for answering my question
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west canyon
Oh okay thanks for answering my question
l pfp
deft zodiac
wot
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muted magnet
can someone help me prove this using a direct proof (Discrete Math)
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can someone help me prove this using a direct proof (Discrete Math)
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muted magnet
<@&286206848099549185>
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earnest perch
can someone help me prove this using a direct proof (Discrete Math)
not sure if this is how ure supposed to prove this but u got 2^4 = 16 cases, u can make a big table with all the different cases to prove that this claim is true
probably not the most efficient way tho, not sure
on the left u got [(q ⇒ p) ^ s]
i believe there are actually only 3 cases where this is true,
in the other cases where this is false, something false implying anything else is always true
so u only have to check the three cases where (q ⇒ p) ^ s to make sure that in these cases the second statement is true
vagrant egret
Find the differential coefficient of $$y=e^{sin(X)}$$
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Find the differential coefficient of $$y=e^{sin(X)}$$
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Night Wølf
vagrant egret
Someone explain me how can I find this, like I already have e here even with a power of sinx, so tbh I don't even know from where to start
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sacred fog
Someone explain me how can I find this, like I already have e here even with a p...
just differentiate it?
vagrant egret
I have become rusty, I don't even have a bit of idea on how just because there is a e in it
vagrant egret
just differentiate it?
Can u explain how?
sacred fog
,, \frac{d}{dx} e^{f(x)} = f'(x)e^{f(x)}
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illuminator3 (#eric4honorable)
sacred fog
chain rule
vagrant egret
Ok understandable
sacred fog
if $h(x) = f(g(x))$ then $h'(x) = f'(g(x))g'(x)$
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illuminator3 (#eric4honorable)
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vast comet
quick question:
if i have a claim to prove/disprove and then show that the negation is false, I have shown the original statement is true, yes? Ty
rare dock
yep
vast comet
cool thanks .close
slate hemlock
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tulip bluff
Can someone help me graph a function? I'm lowkey confused on how to graph this. I j need a visual and I'll probaly get ut
tulip bluff
Limit as x approches 3 f(x) exists but f(3) is undefined
and then Limit as x approaches -4 f(x) does not exist
rapid rain
well, take for example : f(x) = cos(1/(x+4)) defined for x in ]-4,3[
tulip bluff
Wdym?
rapid rain
Limit as x approches 3 f(x) exists but f(3) is undefined
well you want an example of function like this right ?
tulip bluff
yeah
rapid rain
and then Limit as x approaches -4 f(x) does not exist
and this
rapid rain
ok lemme draw it
tulip bluff
thanks
rapid rain
Let's consider this function
As you can see, f(x) goes towards +infinity as x goes to 3
And yet f(3) is undefined because f can only output finite values
tulip bluff
okay that makes sense
rapid rain
Then, for -4
tulip bluff
so would we assume it goes on forever except 3?
rapid rain
"Goes on forever" ?
rapid rain
Yes
tulip bluff
Ok. Whats the righmost line?
rapid rain
Oh it's only f(x) for x > 3
tulip bluff
How do we know it'll look like that?
rapid rain
? You don’t, you just asked for an example that works
tulip bluff
ohh okay I see
rapid rain
So, now for -4
If you look at the limit in -4 starting from the left, it's going straight to +infinity
But if you look at it from the right, it goes down to -infinity
So the limit is not defined at all
rapid rain
so y is going to + infinity and x is going to -infinity
Not exactly
y is going to +infinity from the left of -4, and y is going to -infinity from the right
tulip bluff
oh okay I get it
So for the rightmost side could that line thoertically just be anything? I'm not too sure how you'd find that
rapid rain
I mean you don’t even have to make your function go to infinity
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safe trench
,rotate
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safe trench
What is the end bracket for?
bright trout
i copied it from the question
"is the statement tautological?"
calculator i popped it in spat out this
which makes me think mine is incorrect
safe trench
Where are you incorrect?
bright trout
The last bit, 0 means false no?
safe trench
Yes and?
bright trout
calculator says tftf, i have ftft
safe trench
Order doesn't matter
You are right
If you see carefully
Calculator did FFTT for p which is opposite for yours
And FTFT for q which is also opposite
But if you like at the first row F(p) and F(q) gave T
Which matches with your last row
And when you look at all the rows than they match
bright trout
ohhh
safe trench
So yours is correct
bright trout
true
okay, thank you for pointing that out i was very confused
one more related quesiton
in the tutorial on this stuff i saw we can suddenly add another letter, r, but they don't really explain what it is or where it came from
it's specifically the law of separability - an alternative mode of conjunction
safe trench
what do you know about p and q?
bright trout
translator screwed up the table,
safe trench
r is just another variable like p and q
You see this law is kinda like algebra distributive law
a(b+c) = ab + ac
bright trout
right
ohh so if we had another variable, like r, the table would be filled out for us like it is with p and q?
like you're not supposed to figure out r based on p and q
because everything after it i can totally work out like q ∧ r because you just compare those two already existing
safe trench
Yes
dense arrow
I’m not sure how I graph the line
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fathom seal
Would the answer be what I stated?
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Would the answer be what I stated?
scarlet basalt
can someone check my answer
pulsar cradle
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pulsar cradle
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latent lake
is there any way to solve this question with a different method from the explanation?
latent lake
i tried to do something like making algebra equations with the line y = 2012x/2015
i ended up getting these equations but im pretty sure theyre wrong
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muted raft
Howe would I inhtegrate tcospit?
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Howe would I inhtegrate tcospit?
sudden stirrup
Ok so here you go
onyx glen
integration by parts
sudden stirrup
Took me like 10 min the previous thread closed
I put as much color code so you can easily find where everything is coming from
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muted raft
Why7 is part C 3x-2y-z
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Why7 is part C 3x-2y-z
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ocean sapphire
I've tried solving this for a few hours, and I keep getting lost at the last part where I convert the "and" to "or" statements and vice versa
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smoky cairn
Hi
smoky cairn
i need help on the hypothesis tets for this q
- A clairvoyant claims that he can tell the suit of any card drawn randomly from a standard pack of
52 cards, without of course seeing it face up.
In a test, he succeeds with 4 out of 6 cards. Carry out a test at the 2.5% significance level, to see
whether his claim is realistic.
so far ive stated trials = 6
so sample = 6
h0: he isnt claryvoiant and his chances should be 0.25
h1: he is claryvoitan and his chances are greater than 0.25
how do i move forward
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smoky cairn
P(X ≥ 4) = 0.0376 > 2.5%
thanks but how'd u get the value 0.0376
i dont see it on the chart
actually i do at the very end
so px>=4 can also be done as
torn jolt
P(X ≥ 4) = P(X > 3)
torn jolt
or 1 - P ( ≤ 3)
torn jolt
no its fine to ask
smoky cairn
thanks so much ive been stuck on this for 2 days
the first part is like this
8.You have been given the task of finding student opinion on the wearing of school uniforms in the
sixth form. A number of different methods of collecting a sample are suggested to you. For each of
these determine what sampling technique it is and give at least one advantage and at least one
disadvantage. Remember to consider practical issues as well as mathematical ones.
(i) Select students at random from year 12 and year 13 in proportion with the total number of
students in each of these year groups.
also ive accepted the null hypotheses
since the value is greater than 0.025
torn jolt
So the answer would be at 5 cards, we would consider him as a claryvoiant (with a error of less than 2.5%)
torn jolt
There are two types of sampling methods: Probability sampling involves random selection, allowing you to make strong statistical inferences about the whole group. Non-probability sampling involves non-random selection based on convenience or other criteria, allowing you to easily collect data.
smoky cairn
There are two types of sampling methods: Probability sampling involves random se...
ah ok i completed that q
can i ask u if im right to assume something from this question:
Clinical trials have found that 35% of patients are likely to suffer side-effects from a drug which
treats migraine. A GP prescribes the drug to 15 of her patients each month.
(i) Find the mean number of patients who will suffer side-effects each month.
(ii) Find the probability that in one particular month, fewer than 3 patients will suffer side-effects
ive calculated 15x355 for answer i
and for ii ive done this
one sec
<@&286206848099549185> am I right so far in my approach?
smoky cairn
okok and for ii?
smoky cairn
so starting from 0-2 was correct?
glossy valveBOT
Result:
0.061734095365285
awesome tysm
twin heron
can someone give me the correct answer, book's one doesnt look right
smoky wing
Show your work
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hot herald
are you looking at the correct solutions?
lofty island
<@&268886789983436800>
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fossil condor
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severe basin
An urn contains 10 balls numbered from 1 to 10. We remove six balls randomly and add up their numbers. Let X denote the sum of the numbers of the removed balls. Find the expected value of X.
severe basin
It seems there would be too many cases to consider
Even if I pull out the C's, I'm quite unclear about how I would approach this question
onyx glen
you do not need to know the distribution of the sum of ball numbers
linearity of expectation makes this problem easy
severe basin
Hmm
onyx glen
consider your selection of balls from the urn as ordered, and let $B_i$ be the random variable representing the number on the $i$th ball, for $i=1,\dots,6$. then $X = B_1+B_2+B_3+B_4+B_5+B_6$ and $E[B_i] = 11/2$
glossy valveBOT
Ann
onyx glen
linearity of expectation
onyx glen
no, you're overthinking it again.
you know that for any two random variables X and Y (||under sufficiently "nice" but also technical conditions i don't want to mention||) we have E[X+Y] = E[X] + E[Y], right?
severe basin
yes
onyx glen
right
so if you know the expectation of each B_i
then surely the expectation of X would be their sum
severe basin
I'm not getting it, sorry
onyx glen
$$X=B_1+B_2+B_3+B_4+B_5+B_6$$ therefore $$E[X] = E[B_1] + E[B_2] + E[B_3] + E[B_4] + E[B_5] + E[B_6]$$
glossy valveBOT
Ann
severe basin
For 6 balls, it would be 33.
onyx glen
yes exactly
none of this "oh actually we multiply by 10C6 because i think it's wrong if no factorials ever appear" bullshit
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torn jolt
can someone who understands French help me with this problem? Please
restive kelp
umm, this is an english server, but hope u find someone with the right math&language skills
torn jolt
I hope so too, I didn’t find a french server
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next abyss
So I'm not sure where to continue
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So I'm not sure where to continue
next abyss
I found the derivative
however I'm not sure how to determine what the value of y would be
desert rain
plug in y=1
desert rain
yeah
next abyss
then what would x be
desert rain
solve 1st equation for x
gritty rose
plug in y=1
i think you mean x=1?
next abyss
yea, y=1 doesn't make sense
gritty rose
you still need to find y(1)
next abyss
And I'm not sure how
gritty rose
plug in x=1
next abyss
y=ln(1+y^2)
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worthy ginkgo
Okay so you need to compute y' first. Always remember that the y in the expression is still a function. Then plug x=1
worthy ginkgo
Use the chain rule
next abyss
worthy ginkgo
Yea
next abyss
the one before is just more simplified
worthy ginkgo
Now plug x=1
You'll get an equation involving y'(1)
And you'll need to compute y(1)
worthy ginkgo
plug in x=1
Use that expression
worthy ginkgo
No
That's not what you get
You get
$y'(1) = \frac{2+2y(1)\cdot y'(1)}{1+y^{2}(1)}$
glossy valveBOT
black_couscous
worthy ginkgo
So of you have y(1) it's over
worthy ginkgo
y is a function
next abyss
where do the (1) come from
worthy ginkgo
You apply the function in 1
next abyss
ok, so how do I find y(1)
worthy ginkgo
plug in x=1
Use that
next abyss
I would just get y=ln(1+y^2)
worthy ginkgo
$y(1) = \ln(1+y^{2}(1))$
glossy valveBOT
black_couscous
next abyss
so y is just ln(1+y^2(1)) at 1?
worthy ginkgo
No y(1) is that
next abyss
do I plug in ln(1+y^2(1)) in the derivative where y(1)?
worthy ginkgo
You study the function $f(t)= t - \ln(1+t^{2})$
glossy valveBOT
black_couscous
worthy ginkgo
You find that $y(1)$ must be equal to $0$
glossy valveBOT
black_couscous
next abyss
I just don't understand how we get to that conclusion
worthy ginkgo
**black\_couscous**
After studying this
next abyss
I'm not sure how I would do that
worthy ginkgo
Hint : show that it's always positive by computing it's derivative
That's its graph
next abyss
the derivative would be
worthy ginkgo
Yes
worthy ginkgo
No it's negative between 0 and 1
But the minimum of f is in 1 where $f(1)=\ln(2) \ge 0$
glossy valveBOT
black_couscous
worthy ginkgo
So $\forall x \ge 0, f(x) \ge 0$
glossy valveBOT
black_couscous
next abyss
ok I see
I cant see how it helps though
because this involves implicit differentiation
glossy valveBOT
black_couscous
next abyss
I don't know, still very confusing to me
gritty rose
**black\_couscous**
re-write this as y = log(1+y^2) and solve for y
gritty rose
I don't know, still very confusing to me
what value of y solves ^ equation?
and do you know how couscous got that equation?
next abyss
@gritty rose
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lyric oyster
i want to make sure if i did this right
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i want to make sure if i did this right
light sonnet
Plug back in your values of x
lyric oyster
what do you mean
light sonnet
If you plug back x = 5, into the original equation, it should result in 0, if it doesn't that means your answer was wrong
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atomic grove
ok
atomic grove
350 middle school students signed up for activities after school.
105 signed up for basketball.
84 signed up for soccer.
56 signed up for Legos / robotics.
42 signed up for the math team.
63 signed up for the school play.
whats the percentage of the school play
as a decimal
atomic grove
yaya
wraith river
It gives u 0.09
atomic grove
its wrong
wraith river
how
atomic grove
ayp
where u getting ur stuff from
theres 350 tal students
350 middle school students signed up for activities after school.
105 signed up for basketball.
84 signed up for soccer.
56 signed up for Legos / robotics.
42 signed up for the math team.
63 signed up for the school play.
350 total
atomic grove
i need it converted into a decimal
wraith river
0.10 i think
atomic grove
n
here
try this one
The top four runners in a 100-meter sprint finish in 13.1 seconds, 14.54 seconds, 14.9 seconds, and 15.2 seconds, respectively. What is the mean value of the four runners' time?
________ seconds
bruh
wraith river
Do u know how to find the mean
wraith river
350 middle school students signed up for activities after school.
105 signed up ...
Im stupid its 0.18
I dont know how i did the calculationswrong LMAO
atomic grove
A wedding planner asks guests to RSVP with their dinner preferences before the big day.
35% will likely choose the steak option
27% will likely choose the chicken option
20% will likely choose the vegetarian option
18% will likely choose the fish option
If 300 guests responded, about how many steak dinners will they need to prepare?
About how many chicken options will they need to prepare?
atomic grove
Ill try to help
np