There may be another way of doing that but that's what jumps out to me
#help-36
white rock
would qpr be 76?
uneven linden
That would imply SPR is a straight angle
so probably not
I'd maybe just do law of sines
white rock
sin rule?
uneven linden
sin(QPR) / 200 = sin(45) / whatever you calculate PR to be
uneven linden
Can you find QPR from there?
uneven linden
yeah
tranquil pine
$-7|x + 12| \leq -14$
final saddleBOT
$-7|x + 12| \leq -14$
soft zealotBOT
BabaEagle
cold gorge
Have you done similar problems before?
tranquil pine
yea but im confuised
i divided by -7 and flipped the symbol
then i wrote
-2 ≥ x+12 ≥ 2
is this correct?
final tangle
no
tranquil pine
y
cold gorge
Don't skip steps
final tangle
don't take shortcuts
final tangle
by writing that there's an implementation that -2 is greater than 2, which it is not
final tangle
still wrong
tranquil pine
how do i do this
final tangle
after dividing you'll have
$$|x+12| \geq 2$$
soft zealotBOT
ℝamonov
final tangle
and then if you don't know the identity for the shortcut, go the long route and consider the negative and positive cases
tranquil pine
what does that mean
final tangle
do case work
case 1: x+12 >= 0,
what will the equation be under those conditions
similarly,
case 2: x + 12 < 0
what will the equation be under those conditions
(note that that's actually a bit overkill)
tranquil pine
how do you know to switch the symbol
final tangle
which symbol
tranquil pine
greater than and less than
final tangle
when you do stuff like multiply or divide both sides by a negative value
final tangle
consider doing the long case work, or properties of absolute values, geometric interpretation or identities
final tangle
probably
tranquil pine
ok ty
final tangle
good vids on absolute value inequalities should tell you the process behind reaching that
consider some simpler examples like
|x| >= 5
and
|x| <= 5
how they're different and how they'd be represented on the number line
final tangle
note that though what they've written in the solutions is what you should have
(i don't know whether you had that yourself)
you can not represent it as
-2 ≥ x+12 ≥ 2
tranquil pine
-2 < |x+13 | < 2
and it said it was correct
and i didnt have to switch any symbols
final tangle
you mean -2 < x+13 < 2 ?
tranquil pine
yea
and i got -15 < x < -11
(-15,11)
and it said ok
this is why i am confused
final tangle
it'd be clearer when you|
consider some simpler examples like
|x| >= 5
and
|x| <= 5
how they're different and how they'd be represented on the number line
tranquil pine
yea
final tangle
were you able to do those simpler examples?
final tangle
both are wrong
tranquil pine
why
final tangle
|a| > b does not mean a>b or a>-b
likewise
|a| < b does not mean a<b or a<-b
tranquil pine
oh ok i see
i just read my notes my teacher told me
keep the first one same sign and symbol
then flip the symbol and sign
so x less than a
x greater than -a
final tangle
geometrically the solutions to |x| >= 5
are the values that have a distance greater or equal to 5 from 0
geometrically the solutions to |x| <= 5
are the values that have a distance less than or equal to 5 from 0
tranquil pine
what do u think about what i mentioned
final tangle
sounds wrong
final tangle
also not ideal if you don't understand the theory behind what you're doing
geometrically the solutions to |x| >= 5
are the values that have a distance greater or equal to 5 from 0
final tangle
final saddleBOT
final saddleBOT
Available help channel!
soft kindle
how would I solve for G? I was told to make a parallel line in between both lines to find exterior angles but i dont quite understand. some help would be much appreciated. https://media.discordapp.net/attachments/426033723448885248/1019064280710139974/IMG_4019.jpg?width=683&height=910
final saddleBOT
how would I solve for G? I was told to make a parallel line in between both line...
final tangle
apply some parallel line theorems
soft kindle
we werent taught that yet
soft kindle
we briefly went over it in class for like a minute or so and he didnt really tell us what it was but rather he just showed us
final tangle
google parallel line theorems
and read up on them
it'll give you a clearer idea of what to do here
south aurora
how do you characterize by abstraction?
e.g. Characterize the following set by abstraction: {11, 121, 1331, 14641}
final saddleBOT
how do you characterize by abstraction?
e.g. Characterize the following set by a...
@south aurora Has your question been resolved?
upper kite
,wolf 11^2
soft zealotBOT
upper kite
,wolf 11^3
soft zealotBOT
upper kite
,wolf 11^4
soft zealotBOT
south aurora
i understand the math, but how do i characterize it in terms of {x, y}?
like {11^x} and then something else for y?
we are doing set theory right now so i think along the lines of that maybe
maybe {0<x<4, y=11^x}?
upper kite
maybe {0<x<4, y=11^x}?
look up set builder notation
first the object, then the contraints
{11^x|x integer & 0 < x < 5}
south aurora
okay thank you!
south aurora
i have one last question, could someone help with this please? Prove that there is at most one empty set (i.e., that if A and B are sets with no members, then A=B).
distant hawk
Hint: What is the usual way to prove two sets are equal?
south aurora
I have this in my notes: 1.) Suppose A is a a subset of B. Take arbitrary object x and suppose X belongs to B. Then X belongs to B. Suppose now X belongs to B then X belongs to A. So X belongs to A iff X belongs to B. So A=B. 2.) Suppose A=B. Then A is a subset of B. Similarly, B is a subset of A
final saddleBOT
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final saddleBOT
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@hasty egret Has your question been resolved?
pine root
@hasty egret i can help you if you still require it
final saddleBOT
<@710280671498600508> i can help you if you still require it
pine root
.close
final saddleBOT
hasty egret
<@710280671498600508> i can help you if you still require it
Yes that would be awesome. Please
pine root
right, so we can use the variation formula which is as follows
grim nebula
what even was the problem
pine root
it got deleted...
grim nebula
rip
pine root
@hasty egret repost
hasty egret
pine root
yep
basically you just take a bound and show the variance is less than 40 for all naturals > 1
nic
hasty egret
could you please elaborate more? @pine root
pine root
ok wait no sorry the answer is a lot more complicated than that
final saddleBOT
Available help channel!
dense oasis
plz help
dense oasis
we did this over a week ago and now we have our review and tset tmr
and im completely lost
quick galleon
you need to calculate x and y components of u, v and w
quick galleon
get actual vector form and just add them yeah
dense oasis
and then for the angle ik its tan but of everything individual or together
dense oasis
okok lemme do it rq
ok so for the final x i got -54.82
and y i got 18.53
so the hypotenuse is
55.03
close enough to 57 right?
but for the angle i got -71
what did i go wrong
oh nvm
cause im supposed to subtract form 90
.close
jolly eagle
I apologize for asking again but when converting absolute value into piece wise when do we use the >= or <= signs?
final saddleBOT
I apologize for asking again but when converting absolute value into piece wise ...
final saddleBOT
@jolly eagle Has your question been resolved?
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@jolly eagle Has your question been resolved?
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@jolly eagle Has your question been resolved?
mint orbit
ultimately its not gonna matter, i believe
like
\begin{equation*}
|x| =
\begin{cases}
x & x \leq 0 \
-x & x > 0
\end{cases}
\end{equation*}
soft zealotBOT
jan Niku
mint orbit
thought exercise is to think of like
what happens if you move the equals case from x to -x
hint: whats |0|?
|0| = 0 = -0
@jolly eagle
jolly eagle
|0| = 0 = -0
i see so the sign doesnt really matter because it would work either way?
mint orbit
i see so the sign doesnt really matter because it would work either way?
well its just like
-x and x agree at a place
its where x=0
so then the equality can be shifted between the two in that way
because the equals case in piecewise absolute value is always where the argument equals 0
its sort a special quirk of |x| i guess, or just uhh
i believe this is just a part of functions that are symmetric about 0
so you could say even functions in general
jolly eagle
hm ok cool thank you I think I understand it a bit better now
final saddleBOT
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Available help channel!
eager galleon
hello I need help in inequalities
final saddleBOT
hello I need help in inequalities
modest wigeon
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@eager galleon Has your question been resolved?
misty sky
final saddleBOT
dreamy shadow
,rotate
soft zealotBOT
dreamy shadow
you can think of it as combination of two different situations
P(white or yellow, in either order but not both) = p(white first then yellow) + p(yellow first then white). it might be easier to calculate it in that way
misty sky
Which is 1/10 x 2/9 + 2/10 x 1/9?
final saddleBOT
@misty sky Has your question been resolved?
dreamy shadow
Np man
wait you still confused? 1/10 x 2/9 + 2/10 x 1/9=2/45 is the answer isn't it?
tidal token
Given F: R^4 -> R^3
if I have a basis of ImF as {( 1, 0, 1), (0, 1, -1)}
How do I find the set of values associated with F^(-1)[( 1 0 1)]
final saddleBOT
Given F: R^4 -> R^3
if I have a basis of ImF as {( 1, 0, 1), (0, 1, -1)}
How do ...
tidal token
Given F: R^4 -> R^3
if I have a basis of ImF as {( 1, 0, 1), (0, 1, -1)}
How do I find the set of values associated with F^(-1)[( 1 0 1)]
This is the linear map
<@&286206848099549185>
<@&286206848099549185>
final saddleBOT
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tidal token
<@&286206848099549185>
tidal token
.close
drifting hollow
Hi i need help for this one
at Jay's pizzeria a pizza cost $5 with the first topping, and then an additional 75 cents for each additional topping
if x represents the number of toppings on a pizza, what function represents the cost of pizza with atleast one topping?
wraith crater
So the initial price is $5 and every additional topping cost $0.75. If we have x additional toppings can you think of a way to express this.
fast heart
That's the question reworded 😭
wraith crater
I think the wording is a bit confusing
wraith crater
Hi i need help for this one
at Jay's pizzeria a pizza cost $5 with the first t...
You must have 5 at first so the function is gonna be 5 + something that depends on how many additional toppings you want.
latent cloak
5 +.75x should work yeah?
sorry
5+.75(x-1)
as 5 is the initial cost, with you only adding.75 if there is more than one topping, which is where the x-1 comes from
final saddleBOT
@drifting hollow Has your question been resolved?
median scaffold
after proving that f(x) = x/(1+abs(x)) is indeed bijective, i was asked to find its inverse function f-1(x)
i found two values
f-1(x) = x/(1+x)
f-1(x) = x/(1-x)
is this possible?
final saddleBOT
after proving that f(x) = x/(1+abs(x)) is indeed bijective, i was asked to find ...
void valley
after proving that f(x) = x/(1+abs(x)) is indeed bijective, i was asked to find ...
be careful about |x|, what if x < 0 and what if x >= 0?
median scaffold
be careful about |x|, what if x < 0 and what if x >= 0?
yes thats what i did
and from those two cases i got two expressions of f-1(x)
also f-1(x) goes from ]-1;1[ to IR
void valley
so one of them is for x < 0 and the another for x >= 0
void valley
yes, kind of
stuck field
what's the domain
final saddleBOT
what's the domain
stuck field
of
final saddleBOT
stuck field
tan(2arctan(x))
dawn elk
Please don’t occupy multiple help channels.
final saddleBOT
@stuck field Has your question been resolved?
tranquil pine
whats the answer to the problem
final saddleBOT
whats the answer to the problem
dawn elk
You are given values of a,b,c right
dawn elk
So substitute it in the question
dawn elk
Hmm?
dawn elk
Well in the question it is asked $-(27^2)$
soft zealotBOT
dawn elk
And not $(-27)^2$
grim nebula
yuck
dawn elk
Omg not again
tranquil pine
if you square -27
grim nebula
your colours 🤢
tranquil pine
wouldnt it become postive?
soft zealotBOT
dawn elk
wouldnt it become postive?
Yes it will
grim nebula
the square is done before the negative sign
tranquil pine
Yes it will
so my teacher is wrong
dawn elk
But thats not what it’s asked here
soft zealotBOT
tranquil pine
grim nebula
we do the exponents before we do the signs in front
grim nebula
,w |abc - 27^2 + 6b| where a = 9, b = 4, c = -8
dawn elk
Yes he/she is for 288
soft zealotBOT
soft zealotBOT
grim nebula
,w -2^2
soft zealotBOT
grim nebula
,w -27^2
soft zealotBOT
tranquil pine
HOW
tranquil pine
like
grim nebula
ask wolfram
tranquil pine
no no
grim nebula
because in math notation
dawn elk
Refer here
grim nebula
the exponent is applied before the negative sign
thats just convention
if you want the negative sign included you need brackets
grim nebula
Refer here
thanks deep
dawn elk
\lettern\letterp
soft zealotBOT
dawn elk
tranquil pine
okay oka
grim nebula
oh no i cant even remove that
final saddleBOT
tranquil pine
thanks nerds
dawn elk
Np
grim nebula
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Available help channel!
patent flame
Whats the relevance of ‘exactly 2 days’ in question 2b?
final saddleBOT
Whats the relevance of ‘exactly 2 days’ in question 2b?
patent flame
How does it relate
past kernel
final saddleBOT
Available help channel!
rugged idol
M
tranquil pine
@rugged idol Cannot see any problem here.
Oh ok, now I can.
Okay so now what you have to do is start by taking certain x values and plugging them in to find the y's and graph.
So cause there is -4 there already in the middle as the key term.
Maybe before that you can do -2 and -2.
And after that do 0,1, and 2.
rugged idol
The -4 is wrong
tranquil pine
Okay, then why is it there?
rugged idol
Cus ididnt erase it yet
tranquil pine
Oh okay, got you.
Then do so, and you can use the following values as the x and find the y values to evaluate.
x = -2,-1,0,1,2,and 3.
Then plug those in and solve and tell me what you get it. I will do it on my side as well.
@rugged idol Are you doing it?
tranquil pine
Okay, keep going.
final saddleBOT
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@rugged idol Has your question been resolved?
hushed fable
final saddleBOT
hushed fable
Im not sure how to approach this
hushed fable
Im not sure what to do first
inland bison
Starting expanding and simplify
Like i said, start expanding and simplify the numerator
You will notice that you can further simplify the fractions after that
hushed fable
.close
hushed fable
final saddleBOT
hushed fable
How do I “expand this”
odd parrot
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torpid sequoia
this is just (a+b)^2 from algebra
it looks like you're trying to find the derivative of f(x)=x^2 where x=-1
$f'(-1) = \lim_{h\to 0}\frac{f(-1+h) - f(-1)}h = \lim_{h\to 0}\frac{(-1+h)^2-(-1)^2}h$
is this where you are?
soft zealotBOT
rome of oxtrot
torpid sequoia
if this is whre you are, the next step is to expand the $(-1+h)^2$ term using binomial expansion
soft zealotBOT
rome of oxtrot
radiant spire
final saddleBOT
radiant spire
is this correct?
final saddleBOT
@radiant spire Has your question been resolved?
vast prawn
Sorry but is this the right derivative to my problem
final saddleBOT
Sorry but is this the right derivative to my problem
@vast prawn Has your question been resolved?
final saddleBOT
@vast prawn Has your question been resolved?
brisk otter
Heyo, I am struggling to figure out how to prove the cardinality of the set of prime numbers is equal to the cardinality of the set of even numbers, I don't really know where to start as unlike even numbers to odd numbers I can't just directly map one to the other. Is anyone able to give me a bit of a hint on how I can do this, or perhaps a link to a source that explains it a bit?
final saddleBOT
Heyo, I am struggling to figure out how to prove the cardinality of the set of p...
@brisk otter Has your question been resolved?
brisk otter
<@&286206848099549185> Sorry is there anyone who can help me with this one?
storm scroll
Let f(p)=#{n in P|n<p}
brisk otter
What is the #?
brisk otter
oh right
storm scroll
Let f(p)=#{n in P|n<p}
this is quite literally just another way of saying f(p_n) maps to n where p_n is nth prime
but mire explciitly showing that its a bijection
brisk otter
I understand what you're saying but not entirely how it works
so how does that show it's a bijection? Or more importantly, how do I use that against even numbers
storm scroll
I understand what you're saying but not entirely how it works
test it out with a few primes
brisk otter
alrighty 😛
storm scroll
so how does that show it's a bijection? Or more importantly, how do I use that a...
i mapped the primes to the nsturals
im sure u know a bijection between the naturals and the evens
brisk otter
yes okay
storm scroll
compose them
storm scroll
depending if u jnclude 0 in N or not, you may with ti replace the n<p with n<=p
brisk otter
I do not include 0, thank you though
final saddleBOT
@brisk otter Has your question been resolved?
worn galleon
Hey there,
I have 3 sets
U={2,3,4,5,6,7,8,9,10,11,12,13,14}
A={1,3,5,7,9...} | These are infinite odd numbers
A'={2,4,6,8,10,12,14}
If I get asked something like
Does A∪A' = U? Is it true or false. I'm stuck because A is infinite
Thanks
amber holly
You should use ... notation to indicate that a set is infinite (just now realised that this is irrelevant)
amber holly
Hey there,
I have 3 sets
U={2,3,4,5,6,7,8,9,10,11,12,13,14}
A={1,3,5,7,9...} |...
U doesn't have 1 in it, but A∪A' does
So no
terse dagger
Can someone double check the last one wolfram says it should be diagonalisable but it doesnt work
final saddleBOT
Can someone double check the last one wolfram says it should be diagonalisable b...
terse dagger
,rotate
soft zealotBOT
terse dagger
Matrix multiplication
terse dagger
Doing the last two first leaving the left most
lusty verge
i forgot u have to add them 1 sec ill check it
yeah that looks right
which row is wolfram alpha saying is wrong
terse dagger
Wolfram says it is diagonisable
Meaning it should give the ? Relation
But i get some other matrix
lusty verge
yeah sorry my knowledge of linear algebra only extends to multiplying matrices not diagonisable
final saddleBOT
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final saddleBOT
Available help channel!
wide nova
final saddleBOT
wide nova
any tips on solving this without l'hopital's rule?
final saddleBOT
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@wide nova Has your question been resolved?
vapid crystal
final saddleBOT
vapid crystal
is this reasoning incorrect:
tired walrus
i think there might be a =0 missing in the statement
vapid crystal
correct.
this is what i came up with for the problem: as p is not a perfect cube, p^1/3 is irrational, therefore for b, c ∈ Q\0, b(p^1/3) and c(p^2/3) is irrational. as a+b(p^1/3)+c(p^2/3) =0 as RHS∈Q and rational numbers are closed for addition, LHS is also rational, therefore b(p^1/3) and c(p^2/3) are also rational. b=c=0 and a+0+0=0 therefore a=b=c=0.
im an idiot tho which is why im asking to see if this is incorrect lol tho thx
tired walrus
LHS is also rational
seems ok up to here
therefore b(p^1/3) and c(p^2/3) are also rational.
but then this is bad
vapid crystal
aha
there is no such things along the lines of the converse of closure of rational numbers under addition i.e if a,r∈Q, a+b+c=r then b and c not nessecarily ∈ Q? or im misunderstanding why that is wrong
thanks btw!
wait no im confused. if the LHS i,e a+b(p^1/3)+c(p^2/3) and a is rational then b(p^1/3)+c(p^2/3) must be too. (-a is rational). doesnt this mean both the numbers are rational as the sum of an irrational and rational is irrational and the sum of an irrational and irrational is irrational? therefore both terms must be rational and b=0, c=0.
is this incorrect?
final saddleBOT
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quaint ivy
sum of two irrationnals can be rationnal, example, pi + (1-pi)
final saddleBOT
@vapid crystal Has your question been resolved?
final saddleBOT
vapid crystal
sum of two irrationnals can be rationnal, example, pi + (1-pi)
oh yea that makes sense lol thanks!
final saddleBOT
Available help channel!
pearl jewel
Where do I start if I’m trying to solve this by eliminating X first
final saddleBOT
Where do I start if I’m trying to solve this by eliminating X first
tired walrus
put the equation that begins with -x on the top for convenience
add suitable multiples of this equation to the other two in order to make the x-terms in those cancel out
and you will have your x eliminated
two equations in y and z
which you can solve
and then recover x
pearl jewel
So add multiples to this?
tired walrus
add multiples of (-x+2y+5z=-21) to those two, yes.
tired walrus
ok if i just told you to add that equation itself to each of these
would you understand what i meant
pearl jewel
Yea
tired walrus
ok
and if i told you for example to add 4 times (-x+2y+5z=-21) to (4x+2y-3z=10), would you understand what i meant?
tired walrus
congratulations on completely missing my point!
no, that is not what i said to do.
what i said is to multiply (-x+2y+5z=-21) by 4 and add THAT to (4x+2y-3z=10).
pearl jewel
pearl jewel
final saddleBOT
@pearl jewel Has your question been resolved?
pearl jewel
@tired walrus uhh hello.
tired walrus
alright yeah
now you have 2 equations in y and z
you've eliminated x just as you wanted
pearl jewel
What would be the next step
tired walrus
well do you know how to solve systems of equations in two variables?
pearl jewel
Is that where you eliminate by addition
tired walrus
??
pearl jewel
Never mind, let’s go with No
So now that I have (10y+17z=-74) and (23y+35z=162) what would I do.
@tired walrus 🧍🏿♂️
tired walrus
this is a system of two linear equations in two variables
with some kinda nasty numbers
i would go ahead and power through the arithmetic and do this:
10y + 17z = -24 | * 23
23y + 35z = 162 | * (-10)
winged edge
```
10y + 17z = -24 | * 23
23y + 35z = 162 | * (-10)
```
- Write in standard form then solve for y on one eqn and substitute its value for another
- Multiply both eqn by diffrent numbers such that y coefficents are equal and cancels out leaving the lone variable[z]
choose option [1] or [2]
on the basis of difficult and difficulty only
tired walrus
So I multiply the equation by the number on the right or…
yes, it's short for "multiply both sides of this equation by this number"
in terms of pramad's classification up there my digression is option 2
tired walrus
yes
tired walrus
either one
it doesnt matter
...forgive me for the rashness but it sounds like you have ZERO experience in solving systems of equations in general
youre asking questions that would sound obvious to someone who understands what a system of equations really is
pearl jewel
...forgive me for the rashness but it sounds like you have ZERO experience in so...
Yea we went over it for no more than 15min and the professor gave us this problem to solve for extra credit.
tired walrus
okay so your prof threw you directly into the deep end of the pool is what you're sayin
saying*
on the FIRST DAY you're learning about systems of equations.
that explains it
tranquil pine
can someone help please?
final saddleBOT
can someone help please?
tranquil pine
thin leaf
tranquil pine
I assume you are unable to help
thin leaf
yes sir
final saddleBOT
@tranquil pine Has your question been resolved?
feral cobalt
Here's the original problem:
"From two cities, distance between being 800 km, two trains start travelling towards one-another, and they meet 8 hours after start. If the first starts 3 hours and 20 minutes earlier than the second, they will meet 6 hours after the second train starts. Find the velocity of the faster train."
final saddleBOT
Here's the original problem:
"From two cities, distance between being 800 km, tw...
feral cobalt
I'm at systems of linear equations
ok so I got x+y=100
S = v * t
S distance, velocity, time
800 = v * 8
v = 100
so x+y=100
then it's 6y=800
but how do I put x
in terms of x being the first train that starts 3 hours and 20 minutes earlier
my textbook says 4 hours and 20 minutes earlier = 37/3
I'm incredibly confused how 4 hours and 20 minutes earlier becomes 37/3
or 12 1/3
final saddleBOT
@feral cobalt Has your question been resolved?
feral cobalt
hi! I can try to help.
ok so look, I have to go
I will look into this when I get home
if you could, DM
or w/e is more comfortable for you
I'm calling this a day
buh-bye for a few hours
gonna let this close due to timeout
clever surge
buh-bye for a few hours
ok! I'll let you know later!
final saddleBOT
@feral cobalt Has your question been resolved?
tranquil pine
Here's the original problem:
"From two cities, distance between being 800 km, tw...
use the d = rt
there are two ways to go about it.
- either you use relative speed (the distance between the gap) or you solve them individually.
final saddleBOT
use the d = rt
there are two ways to go about it.
1. either you use relative sp...
@tranquil pine Has your question been resolved?
feral cobalt
use the d = rt
there are two ways to go about it.
1. either you use relative sp...
look, I know
just read
im tired
tnx
tranquil pine
in terms of x being the first train that starts 3 hours and 20 minutes earlier
the convention ratio is always equal to one. ie. 1hour = 60minutes can be written as 1hour/60minutes. Now the clock time is 4hour + 20minutes, so we multiply by ratio 1/60 so we get 4+ 20*(1/60)= 4+ 20/60 = 4 + 1/3 we all know 1/3 = 0.333 hence the time = 4.333
you can also do it like this
find the lcm: 12
(12x4)/12 + 4/12 = (48+4)/12=52/12 now remove a factor of 4 = 13/3hrs
feral cobalt
the convention ratio is always equal to one. ie. 1hour = 60minutes can be writte...
I'm very tired and it's late
I will read up tomorrow
close thread if you will
thank you!
tranquil pine
I'm very tired and it's late
I am interested in the answer, but good night.
feral cobalt
I am interested in the answer, but good night.
will DM you tomorrow
signal flame
Hey guys I need help on my hw I can't seem to figure out how to get the fraction for E can anyone help
final saddleBOT
Hey guys I need help on my hw I can't seem to figure out how to get the fraction...
tranquil pine
B could be any decimal less than less but greater than 0. however, B is greater than A and C.
E could be any decimal number between greater than 2 but less than 3.
tepid snow
ur right with guessing b is 0.5
tepid snow
E could be any decimal number between greater than 2 but less than 3.
i dont think they want it that precise man
its a number line
tepid snow
I think b is 1/2 but idk what e is
e is in the middle of 2 and 3
tranquil pine
there is are infinite number between them
tepid snow
so what is the number halfway between 2 and 3
tepid snow
there is are infinite number between them
yes but this is too complicated
tranquil pine
i dont think they want it that precise man
the question said could.
tranquil pine
yes but this is too complicated
She need to estimate.
signal flame
so its D?
tepid snow
She need to estimate.
exactly and 0.5 * 2.5 is 1.25 which is d
signal flame
ohhh ok thank you guys so much
that wasn't that hard idk why I have trouble with this types of things
tranquil pine
exactly and 0.5 * 2.5 is 1.25 which is d
Sometimes the diagrams caan be tricky.
to be safe test extreme case.
tepid snow
that wasn't that hard idk why I have trouble with this types of things
nah dw
tepid snow
to be safe test extreme case.
yeah but its a number line man
not like some complex roots of unity argand diagram
final saddleBOT
tranquil pine
yeah but its a number line man
Normally simple questions are the trickiest
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Available help channel!
leaden orbit
Can someone help me with part b? I know to isolate so that z = 0, but idk how to ... apply that
final saddleBOT
Can someone help me with part b? I know to isolate so that z = 0, but idk how to...
zenith pollen
projection just means ignore the z part, so just describe <tsqrt(1-t^2),t^2>
final saddleBOT
@leaden orbit Has your question been resolved?
violet furnace
final saddleBOT
gleaming bramble
NPV for population 1 is 0% as everyone in population 1 has a certain disease
NPV for population 2 is 100% as no one has the disease
violet furnace
ok
violet furnace
NPV for population 1 is 0% as everyone in population 1 has a certain disease
NP...
your a blesssing
gleaming bramble
gleaming bramble
mm u have to make a table for both of em
has disease no disease
test positive ur values ur values
test negative ur values ur values
like this
straight forward
gleaming bramble
yuh
mighty glen
Can someone explain the difference between part a and c
final saddleBOT
Can someone explain the difference between part a and c
mighty glen
am I blacklisted
pine root
nah u aint, the velocity vector isnt the equation of the tangent line
tangent line is 1D function of x, velocity vector is 2D function of t_0
final saddleBOT
@mighty glen Has your question been resolved?
loud gust
Hey, I have a question regarding composition of functions.
Consider functions f and g such that f of g = sqrt(x^2 + 1) - 1. If g(x) = x^2 + 1, then what's the value of f(4)?
So, f(x^2 + 1) = sqrt((x^2 + 1)^2 + 1) - 1)
x^2 + 1 = 4 ... x = sqrt(3)
Then, sqrt(17) - 1. But, the answer is 4.
I don't see what I did wrong?
final saddleBOT
Hey, I have a question regarding composition of functions.
Consider functions f ...
marsh temple
i think you're misunderstanding the notation a little
you claim to be looking at f(x^2+1), however the only function you have at the moment is f(g(x))
you first need to extract the function f, and only then can you look at trying to evaluate f(4)
@loud gust
loud gust
@marsh temple But, if you plug in sqrt(3), you get f(4)?
marsh temple
plug in sqrt(3) into what?
marsh temple
i mean sure, if you plug in sqrt(3) into g then you get 4
but you don't know what f is
I think the crux of your issue lies in this line
So, f(x^2 + 1) = sqrt((x^2 + 1)^2 + 1) - 1)
f(g(x)) = sqrt(x^2+1)-1
However, g(x) = x^2+1. If we sub this into the left-hand side of the original equation, we get:
f(x^2+1) = sqrt(x^2+1)-1
or, if it's more readable, f(g(x)) = sqrt(g(x))-1
loud gust
I just don't understand why if you have f(g(x)) = sqrt(x^2 + 1) - 1 that you can't just set g(x) = x^2 + 1 such that f(x^2 + 1)) = sqrt((x^2 + 1)^2 + 1) - 1 so that you have function f by itself.
Then you can just set x^2 + 1 = 4 and get sqrt(3). Then, f((sqrt(3))^2 + 1) = f(4) = sqrt((3 + 1)^2 + 1) - 1 = sqrt(16 + 1) - 1.
marsh temple
you're making two different substitutions
in the equation:
f(g(x)) = sqrt(x^2+1)-1
there is no g(x) on the right hand side
what you're doing is making the substitution x = x^2+1
loud gust
Yes, but if g(x) = x^2 + 1, shouldn't x = x^2 + 1 as seen here f(x^2 + 1)?
marsh temple
again, that's two separate substitutions
in the first case, you're replacing g(x) with its definition
however, x and g(x) are not the same object, and thus you can't make the same adjustment and say that they're equal
loud gust
@marsh temple I think I see now. I'm just replacing g(x) with x^2 + 1, but I'm not constructing a new function. The function is already given. So, f(x^2 + 1) = sqrt(x^2 + 1) - 1 and then I'm able to plug in sqrt(3) to get 1.
marsh temple
if that helps you think about it, sure
the main takeaway should be that saying g(x) = x^2+1 is not the same thing as saying x = x^2+1
final saddleBOT
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Available help channel!
half canopy
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wraith crater
Have you got a diagram?
half canopy
I have no idea about 1 but for number 2 yes I drew the triangle diagram
wraith crater
It’s like an angle measurement but starts from north
North is 0 degrees
Then go clockwise
half canopy
160
half canopy
ohh that makes sense
wraith crater
Yeah so 160 is between south and east
half canopy
what about the 2 cm long part
wraith crater
I think that’s just using a ruler
wraith crater
Alright
wraith crater
I’ve honestly never seen W60S before
No idea what it means
Maybe that means 60 degrees below west?
half canopy
well north is 0 and 360
wraith crater
I think it means between west and south
and 60 degrees below west
So 210 degrees
But I could be wrong and it’s the other way around
So 60 to the right of south
240 degrees
For b can we send me the sketch?
I’m in a bath rn lol
wraith crater
Give me a sec I’ll try to draw something
half canopy
no
wraith crater
Or 310
half canopy
that s single vector
a
den u add the other vector
80kmh from the easr
east
and create a triangle with it
half canopy
You agree with my awesome diagram?
yes but theres problem
the wind is coming from the east
wraith crater
Oh
half canopy
so that means its going west
wraith crater
Damn it
half canopy
the bath distracting you lol
wraith crater
Here we go
half canopy
yes
wraith crater
Then cosine rule apply heee
wraith crater
$$ R^2 = 80^2 + 450^2 -2(80)(450)\cos(40)$$
soft zealotBOT
Pure
half canopy
since i saw east as a stright line i thought it was 90
so 90 plus 40 would give me 130
but yea its just 40 because the 80 doesnt have an angle
half canopy
is that a 90?
half canopy
why
half canopy
we only need the inside angle
half canopy
im lost lol
half canopy
ohhh
wraith crater
No the z pattern doesn’t apply here
half canopy
it can
here ill show you
i said 90 because the looks like a right angle
so 90 plus 40 = 130
wraith crater
I think it’s 210 bearing
half canopy
ok thanks
final saddleBOT
Available help channel!
vagrant smelt
Ok
vagrant smelt
E=mc2
vapid crystal
huh?
marble wave
void crest
amazing
vagrant smelt
Lol
void crest
how did u derive that
void crest
yea how did u find out
vapid crystal
just appeared to them like Kubla Khan 😂
final saddleBOT
@vagrant smelt Has your question been resolved?
autumn siren
help pls
vapid crystal
help pls
what is the probability that a player gets one of the duplicates? what about getting the other too?
autumn siren
what is the probability that a player gets one of the duplicates? what about get...
wouldnt that be (13/52)^2?
vapid crystal
close but no. lets say we have two cards labelled 1a and 1b. what is the probability that a specific player has card .1a ? 13/52. what about card 1b too? 12/51 (12 cards other than 1a from a deck containing card 51 cards). for 4 players p(a a player has both duplicates)= 4*13/52*12/51=12/51
vapid crystal
wouldnt that be (13/52)^2?
youre neglecting to acknowledge that receiving one duplicate removes one card from the deck and one spot to receive the other duplicate for a player
this can also be also thought as follows: a player must receive one of the duplicates because every card must be given away. this reduces the deck size by 1 and the spots of the player by 1. so 13-1/52-1=12/51
autumn siren
youre neglecting to acknowledge that receiving one duplicate removes one card fr...
ahhh true, but why multiply it by 4 if its for one person
vapid crystal
because this is the probability for one specific player, say player 1. but there are 4 players.
any of the 4 players can receive the two duplicates
autumn siren
because this is the probability for one specific player, say player 1. but there...
so wait like combinations?
4C1?
vapid crystal
P(ANY player has two duplicates) = P(p1 has two duplicates) + P(p2 has two duplicates) + P(p3 has two duplicates) + P(p4 has two duplicates)
vapid crystal
4C1?
what is P(px has two duplicates) = P(px has duplicate 1) * P(px has duplicate 2) = 13/52 * 12/51
P(ANY player has two duplicates) = 13/52* 12/51 + 13/52* 12/51 + 13/52*12/51 +13/52*12/51
vapid crystal
no problem!
jovial ermine
Hello, I was going over polar coordinates and it seems to me that the difference between the argument and principal argument is that the argument has an infinite number of values whereas the principal argument is confined to -π to π. The reason I think this is because it would explain the following diagrams which show that the argument is always between -π to π.
- But if this is the case my question is why do we restrict the interval of the principal argument to -π to π?
- Also why do we convert from cartesian to polar coordinates? In what cases are polar coordinates better?
(I think this is to represent events where objects move in circular paths but if there are other reasons I would like to hear about them)
Thanks!
final saddleBOT
Hello, I was going over polar coordinates and it seems to me that the difference...
inland bison
principal argument is just defined to be in that interval, nothing more. However, there is no such thing as a principal argument in polar coordinates, there is just r and theta, and theta, in a way, has no restrictions
the point (1, 1) for example can be represented as (sqrt(2), pi/4) or (sqrt(2), 9pi/4) whichever you want
you are most probably referring to the argument of a complex number here
jovial ermine
principal argument is just defined to be in that interval, nothing more. However...
oh so for polar coordinates we care about the argument θ instead of the principal argument?
jovial ermine
you are most probably referring to the argument of a complex number here
yes that's what I was currently reading 👍
inland bison
no, we really do not, we just only care about what is the angle between the positive axis and that number, that's all, argument in polar coordinates does not matter that much since they dont really give us much use
jovial ermine
no, we really do not, we just only care about what is the angle between the posi...
does argument help us convert between polar coordinates to cartesian coordinates?
inland bison
when representing complex numbers, we are drawing vectors and stuff a lot more, so that's why we talk about arguments of complex numbers
for polar coordinates, we just use it as a tool to draw curves that are way to complicated to represent with just x and y
not just that, but also it acts as a way to simplify the way we can represent a curve. For example take the circle x^2+y^2=1, and i just want to find some random points on this circle, say the point that is pi/2 from the positive x-axis. This is gonna take me some arithmetic to do, subbing in values and stuff, it's tiring. By using polar coordinates, the equation of this circle becomes r=1, this basically means my set of points has the radius of 1 from the origin, and the angle that it makes with the positive x-axis is any angles i like. So that means the point that is pi/2 radians away from the positive x-axis is (0, 1)
this is probably the simplest example i can find that make use of polar coordinates. And as you see, it barely uses the concept of "argument"
theta is just an angle at the end of the day
there are more beautiful curves than just circles, for example the rose curve or limacon, you can check it out online if you want
these curves definitely are not very nice when written in terms of y and x
jovial ermine
not just that, but also it acts as a way to simplify the way we can represent a ...
thanks for the example, its good to know that polar coordinates makes calculations and equations simpler
jovial ermine
there are more beautiful curves than just circles, for example the rose curve or...
ill check these out
Thanks for taking the time to explain this, Waler!
.close
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inland bison
np
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Available help channel!
random scaffold
final saddleBOT
random scaffold
in this integral, when you do u = 1/x and du = -1/x^2dx
how do you include the negative when 1/x^2 here is positive?
shell mountain
du = -1/x² dx right?
random scaffold
If I remember correctly, when you 'add' a value, you needed to divide by it on the outside of the integral