anw
#help-0
ocean sealBOT
ocean sealBOT
ocean sealBOT
ocean sealBOT
ornate condor
u can c how thrs only 1 soln with this for k in int
upper escarp
lone heartBOT
upper escarp
can soemone help check if my ans is ok?
little drum
dude... with 3, 5, 7, etc. k(k+1) will also have an odd factor which we do not want...
anyways, bring it to another ch. if you want to talk
lone heartBOT
@upper escarp Has your question been resolved?
upper escarp
On second question only 2 new sets appear
wdym?
prime badge
what do you mean what do i mean
i mean 28 is right for first and 95 is unjustifiably too big for second
upper escarp
shouldnt it be 10c2 x 8c2 x 6c2 x 4c2 x 2c2
prime badge
i don't know what that is
it's all the sets from (1)
and 2 more
the last question I don't understand, all the statements seem to be wrong, except "one has more tiles than the other" but it's not from pigeonhole?
no wait there's 10
it's the last statement that's true
lone heartBOT
@upper escarp Has your question been resolved?
alpine sable
i need help
lone heartBOT
i need help
amber obsidian
i need help
Usually, people share a question which they need help on
alpine sable
wait
trim wagon
Okay
trim wagon
Post screenshot, don’t make helpers download files
alpine sable
Post screenshot, don’t make helpers download files
trim wagon
Okay so which one?
alpine sable
Okay so which one?
2 and 4
trim wagon
Okay so lets start with 2
alpine sable
yes
alpine sable
aha
trim wagon
So tell me what is it?
alpine sable
i dont know
trim wagon
Umm then idk how did they ask you this, you should learn finding areas of triangle, square, rectangle…etc first
alpine sable
its not a triangle its a prism
alpine sable
okay im gonna fail but than k u
lone heartBOT
@viral field Has your question been resolved?
small tide
i have a question
lone heartBOT
i have a question
lone heartBOT
small tide
.reopen
lone heartBOT
✅
small tide
evaluate this and give ans in Standard form
manic pecan
uhm do you know power rules?
small tide
yea
manic pecan
4x10^-4 + 3x10^-3
just arrange one of them so they have the same exponent
for example 0.4x10^-3 + 3x10^-3
then you can just add 3 and .4 and you get 3.4x10^-3
lone heartBOT
@small tide Has your question been resolved?
autumn plank
hi
autumn plank
does anyone know how to do this?
I thought of (e^bt)' = b * e^bt * ln(e) = b * e ^bt
but that doesnt seem to be the answer seeing the hint
tall topaz
That is the answer
tall topaz
Differentiate e^tln(a)
autumn plank
could you help me doing that
because I wanna know what I'm doing and I got no clue how to work that out
tall topaz
I thought of (e^bt)' = b * e^bt * ln(e) = b * e ^bt
Refer to this
autumn plank
where b is a constant?
tall topaz
t is your variable here and ln(a) is a constant
tall topaz
where b is a constant?
Wdym?
tall topaz
Yeah
autumn plank
I thought of (e^bt)' = b * e^bt * ln(e) = b * e ^bt
here
b is a constant
in the formula e^bt
tall topaz
Yeah
tall topaz
Yeah
autumn plank
.close
lone heartBOT
autumn plank
Thanks x
tall topaz
Np
lone heartBOT
Available help channel!
wintry oyster
is this asking me what x can be or what 4x can be?
lone heartBOT
is this asking me what x can be or what 4x can be?
wintry oyster
im just listing the possible elements in the set
but the (X such that 4x is in intergers, |4x-3| <= 2) is not making sense to me
marsh rapids
but the (X such that 4x is in intergers, |4x-3| <= 2) is not making sense to me
find all the real numbers x such that 4x is an integer less than 2 away from 3. Does that make more sense ?
wintry oyster
no, are you just assuming its all the real numbers since its not specified?
tacit arch
no, are you just assuming its all the real numbers since its not specified?
(4) can be further elaborated as
${ x\in \R \ : \ 4x \in \Z, |4x-3| \le 2}$
ocean sealBOT
riemann (eric tao for honorable)
tacit arch
e.g. obviously x = 0.25 is in that set
wintry oyster
this seems really hard to calculate without a calculator
is that supposed to be like that?
tacit arch
it's a very relatively small set you can write out by hand all elements
tacit arch
this seems really hard to calculate without a calculator
it's not
wintry oyster
if x can be any real number...? maybe im over thinking this?
so like the set is just 2 elements i see that but how exactly would you know that without trying 40 other numbers like 1,2,3,4,5,6,7,..etc
4(1) -3 =1 so doesnt that fit the criteria?
(4(1)) is an integer, x is a real number. and the abs of the equaltion when plugged in is less than or equal to 2
tacit arch
if x can be any real number...? maybe im over thinking this?
you should just work backwards from 4x = to some integer
tacit arch
4(1) -3 =1 so doesnt that fit the criteria?
1 is in the set, yes
tacit arch
so like the set is just 2 elements i see that but how exactly would you know tha...
you use the inequality to stop you as well. expand it into 2 inequalities
wintry oyster
can you explain what you mean by expand it into 2 inequalities?
tacit arch
$|x-a| < b$ means $-b < x-a$ and $x-a < b$
ocean sealBOT
riemann (eric tao for honorable)
tacit arch
can you explain what you mean by expand it into 2 inequalities?
have you seen this?
https://www.basic-mathematics.com/solving-absolute-value-inequalities.html
wintry oyster
Yea i understand that
and thats what i use to make sure i build the sets making sure i include the negative numbers x could be because abs will still be a positive int
tacit arch
so like the set is just 2 elements i see that but how exactly would you know tha...
right. so does that answer your question here?
if not, just start calculating and it should
wintry oyster
It does, however, isnt there an infinite number of integers i could try? per the instructions i need to make the set inside of brackets so i cant just si like -1 < 4x < 1 or something like that. i need to list each element. and in the scenario that x can be any number between wont that be impossible to list every single element or to calculate every element lol by hand i mean
in general i think the answer is -2 <= 5x-2 <= 2 i just dont know if its that simple or im not thinking of this correctly
lone heartBOT
@wintry oyster Has your question been resolved?
lone heartBOT
@wintry oyster Has your question been resolved?
barren elbow
lone heartBOT
barren elbow
2sin(2theta) = 2(2sin(theta)cos(theta) = 4sin(theta)cos(theta)
= tan(theta)
how do I go from here
ooh
= sin(theta)/cos(theta)
autumn pasture
yes
barren elbow
4sin(theta)cos^2(theta) = sin(theta)
autumn pasture
yes
barren elbow
4cos^2(theta) = 1?
trim wagon
Yes
autumn pasture
okay
autumn pasture
4cos^2(theta) = 1?
wait actually no
barren elbow
cos(theta) = +-1/2?
autumn pasture
you don’t cancel the sin
trim wagon
4sin(theta)cos^2(theta) = sin(theta)
Rewrite it as 4sin(theta)cos^2(theta) - sin(theta) =0
barren elbow
wait theres a difference of two squares in here as well I think
barren elbow
oh
autumn pasture
Rewrite it as 4sin(theta)cos^2(theta) - sin(theta) =0
you have this
do you see anything common
barren elbow
I got to sin(theta)(4cos^2(theta)-1) = 0
barren elbow
sin(theta)(2cos(theta)+1)(2cos(theta)-1) = 0
trim wagon
Yes
autumn pasture
🧁
trim wagon
So you have
sinθ=0 or cosθ=1/2 or cosθ=-1/2
barren elbow
yh got that thanks!
trim wagon
lone heartBOT
@barren elbow Has your question been resolved?
wet patio
lone heartBOT
wet patio
Could someone explain to me what the Squeeze Theorem is and how i apply it to this question?
lone heartBOT
@wet patio Has your question been resolved?
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@steep river Has your question been resolved?
turbid kestrel
can someone help me with this?
lone heartBOT
can someone help me with this?
lone heartBOT
@turbid kestrel Has your question been resolved?
tacit arch
the $x^2 - 16$ in the square root suggests some type of trig function times 4. which one did you try?
ocean sealBOT
riemann (eric tao for honorable)
lone heartBOT
@turbid kestrel Has your question been resolved?
final badge
How to find the equation of the horizontal asymptote?
lone heartBOT
How to find the equation of the horizontal asymptote?
final badge
snow furnace
do you know what exponential functions look like?
and do you know the transformation rules
final badge
do you know what exponential functions look like?
no?
alpine sable
need help Q. 13
lone heartBOT
need help Q. 13
heady pollen
if we have a given x, then f(x)=y
so if we have f(-2)=7
then we know that for x=-2, y=7
so the point (-2; 7) lies on our graph
so we get the points
(-2, 7) and (2, -1)
alpine sable
It's not required to make a graph
heady pollen
i know
but still
now we start by calculating a
a is the slope or gradient of f
do you know how to calculate the slope of a line?
heady pollen
$a=\frac{y_{1}-y_{2}}{x_{1}-x_{2}}$
ocean sealBOT
~Martin
heady pollen
(7-(-1))/(-2-2)=8/-4=-2
so we get a=-2
so we have
f(x)=-2x+b
now note that we have three variables in this equations: x, y and b
however, we know points on the graph which provide us x and y
therefore we can for example put (-2,7) into the function
so we get
7=-2(-2)+b
or with the other point we would get
-1=-2(2)+b
both will lead to the same solution for b:
b=3
so in total we have
a=-2 and b=3
f(x)=-2x+3
heady pollen
you're welcome^^
alpine sable
.close
paper holly
how do i write this as a diff equation?
lone heartBOT
how do i write this as a diff equation?
paper holly
abstract fractal
Rate of change of mosquitos = rate mosquitos are produced - rate mosquitos are removed
paper holly
Rate of change of mosquitos = rate mosquitos are produced - rate mosquitos are r...
right but i'm having trouble finding the mosquitos produced part
dp/dt = produced - 30000
abstract fractal
You know that the rate mosquitos are produced is proportional to the current population
In particular, it doubles
That means if there's x mosquitos now, then another x is added on
paper holly
That means if there's x mosquitos now, then another x is added on
right so like p(t)/something?
paper holly
and that something should have something to do with time? because dp/dt is pop/time and p(t) is just pop?
abstract fractal
No
paper holly
If the population is P one day, what's the rate of increase that day?
2^(1/7)?
abstract fractal
Where's that coming from?
The rate of increase in one day is just the number of mosquitos being added that day
paper holly
i meant like 2^(1/7)p(t)
abstract fractal
If there's P mosquitos, and the population doubles every day, how many mosquitos are added
abstract fractal
i meant like 2^(1/7)p(t)
Why 2^(1/7)
paper holly
it doubles every week
abstract fractal
OH
I don't think it's 2^(1/7) though
Because it's not 2P when doubling every day
We can find a by assuming ideal conditions though
dP/dt = aP
And take advantage of the doubling every 7 days
paper holly
We can find a by assuming ideal conditions though
what do you mean by ideal conditions?
and how would we find a? Our final equation would have two constants then
abstract fractal
I mean by assuming the mosquitos aren't being eaten
paper holly
well then p(t) should just be 2^t * p(0), no?
abstract fractal
The second constant will cancel when finding a
paper holly
where t is in weeks
abstract fractal
We don't care about finding p(t) here
Just finding the constant a
p(t) isn't meaningful since it's assuming conditions that aren't relevant
I.e. not being eaten
There's probably an easier conceptual way to find a rather than solving an equation, but i don't feel like racking my brain to find it
paper holly
ln(|p|) = at + c
p = +- e^c*e^at
p = k * e^at```now how would we find a? plugging in t=0 would just get rid of a
i don't think we need the a there
abstract fractal
Consider the ratio between the populations at t = 7 and t = 0
paper holly
for the rate of change, dp/dt, it is p(t+7)-p(t)/(t+7-t)
but the p(t+7)-p(t) is growing so the rate of change is also growing
abstract fractal
We don't need the slope formula
paper holly
my point being
abstract fractal
Find P(7)/P(0) and set it equal to 2
paper holly
right but we don't know what p(t) is
abstract fractal
We know what it is in terms of k and a
paper holly
bro i am 90% sure that (even if this method of yours is correct) is not the method they intended
we just need to find an equation for the mosquitos produced
abstract fractal
Well, considering the answer for a I got, I'm not sure how you're gonna do it otherwise
paper holly
pop it in there
abstract fractal
It's got a natural log in it
abstract fractal
we just need to find an equation for the mosquitos produced
And the equation for the mosquitos produced is aP, which means we need to know a
paper holly
i am super confused
abstract fractal
The rate that mosquitos breed is proportional to the population
That means it's aP for some constant a
We need to find a
paper holly
well then p(t) should just be 2^t * p(0), no?
i still think we have to do something with this
paper holly
That means it's aP for some constant a
wait where did the -30000 go?
abstract fractal
You can use that, and I just did it, but imo it's easier to just take the ratio of P(7)/P(0) for the equation we found earlier and set it to 2
paper holly
oh right, nevermind
abstract fractal
And by "I just did it" I mean on a paper, not in the chat
paper holly
And by "I just did it" I mean on a paper, not in the chat
yeah i figured
did u get a ln(2)/7?
abstract fractal
Yes
abstract fractal
So the rate of mosquito production is ln(2)/7 P
paper holly
because the ln(2) and integral of 2^t would cancel
i mean the ln(2) term that comes out of it would cancel
abstract fractal
Did you do the ratio of terms to get that, or did you get it by taking the derivative of P(0) * 2^(t/7)?
paper holly
Did you do the ratio of terms to get that, or did you get it by taking the deriv...
ratio, the method u told
abstract fractal
Well, you can also do it by taking the derivative of that equation, if you're curious
paper holly
yeah
abstract fractal
So, now you know the differential equation, and I presume you can solve it
paper holly
okay so dp/dt=ln(2)*p(t)/7 -30000 ?
abstract fractal
Yes
paper holly
one thing i don't get
dp/dt is pop over time but p(t) is just pop
shouldn't it have something to do with time too?
paper holly
but it is still the population, dp/dt's units would be pop/time
abstract fractal
The more mosquitos there are, the faster mosquitos reproduce
Then I suppose that ln(2)/7 has units 1/time
alpine sable
Can someone help me please idk this and I’m at work and it’s due tonight
alpine sable
lone heartBOT
@alpine sable Has your question been resolved?
wet patio
lone heartBOT
lone heartBOT
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lone heartBOT
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copper chasm
Help
lone heartBOT
@copper chasm Has your question been resolved?
runic trench
tacit arch
(5,3) means the x coordinate is 5 and y coordinate is 3
5 doesn't change. Only the 3 does
How does the 3 change?
Describe it with numbers
This is completely different
Did you finish this one?
The example has very little to do with your problem
It's also linear algebra
Or geometry
5 stays 5
3 becomes 6
5 is the x coordinate
3 and 6 are the y coordinate
lone heartBOT
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raw citrus
These are two probability proofs that I am having some trouble with. I think I have the first one down, but the second is confusing to me, could someone help?
ornate condor
wait
raw citrus
raw citrus
I wrote it where it is if and only if
raw citrus
Alright
harsh silo
wait can i send a question rq, no one replied on the other one?
raw citrus
Alright, I'll try it
ornate condor
wait can i send a question rq, no one replied on the other one?
just go to another help channel
its rng
harsh silo
lmfao
raw citrus
Could I possibly end up getting P(A)P(B) < P(AB) and then divide the P(A)?
ornate condor
yea thats kinda what u are supposed to do
u can do it one step if u want
just mention that u can do it as they are both >0
rose sigil
hmm I actually don't think that's quite right for the first one
raw citrus
hmm I actually don't think that's quite right for the first one
How is it done then?
rose sigil
something can have probability 1 without being the whole sample space
raw citrus
Oh I see
rose sigil
so this isn't right
rose sigil
I think A and B are independent iff P(B) = 1 is right
it's a little unclear that you're trying to show that though
raw citrus
So I shouldn't say that B must be the universal set?
rose sigil
no, I wouldn't say that
rose sigil
btw how do uve a purple heart in name
ummm I can't remember lol, maybe just copy paste the emoji?
raw citrus
btw how do uve a purple heart in name
Using a red heart will make the colors the same
raw citrus
no, I wouldn't say that
I'm a bit lost then
rose sigil
so I'd probably remove that part about B being the universal set entirely
raw citrus
Alright
rose sigil
and maybe rewrite this a little bit
maybe something like
P(AB) = P(A)P(B) ⇔ P(A) = P(A)P(B) P(AB) ⇔ P(B) = 1
raw citrus
Alright
rose sigil
also this is minor but you have proof: ...
but it's not clear what you're writing a proof for
until the end I guess
rose sigil
or write what you're proving before
lone heartBOT
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lone heartBOT
can anyone help me with this
amber obsidian
can anyone help me with this
Is this from differential equations or is calculus?
lone heartBOT
@shell mortar Has your question been resolved?
shell mortar
Is this from differential equations or is calculus?
its from a physics problem in which i have to find the angular velocity in terms of theta when theta=pi/6
the angluar acceleration has been given which is
alpine sable
the angluar acceleration has been given which is
Rewrite tan theta
Into sin/cos
Then rest will be obv
flat holly
lone heartBOT
sinful ether
help. i do not understand why the couple moment is positive like this
silk quiver
hello
flat holly
@sinful ether sorry, can you take another channel instead? this one is occupied
sinful ether
sorry
flat holly
I need help with part 1
lone heartBOT
@flat holly Has your question been resolved?
flat holly
<@&286206848099549185>
lone heartBOT
@flat holly Has your question been resolved?
flat holly
<@&286206848099549185>
ornate condor
u can first find
AM, using area of triangle
with AM and AE with a right angle, u can find angle AME
part 2, CMD is just AME
with sin rule u can find MCD and thus MDC
AB should be trivial, using cos rule, uve AD, BD and ADB
lone heartBOT
@flat holly Has your question been resolved?
flat holly
AB should be trivial, using cos rule, uve AD, BD and ADB
thank you
lone heartBOT
ornate condor
❤️
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wanton kiln
Just to be sure I've understood correctly:
$D_8 \leq D_{16}$
right?
ocean sealBOT
CoffeeMan
snow furnace
In what context?
worn fox
Is D8 square or octagon
ocean sealBOT
CoffeeMan
lone heartBOT
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silent sage
Why does the given formula necessitate the equivalence of the coefficients of x and y respectively for two lines to be parallel?
silent sage
As such is there any other way to go about it other than converting the equation as shown in the example every time to use the formula?
gilded citrus
Why does the given formula necessitate the equivalence of the coefficients of x ...
the ratio of a and b must be equal if they are parallel and you can always multiply/divide one of the equations to make their a's and b's equal
slender gull
As such is there any other way to go about it other than converting the equation...
Have you seen the proof of the formula?
Do you know where the formula came from?
Because if you do, then it gets fairly obvious why the a and b terms MUST be the same.
silent sage
No, for both the questions, Should google it I suppose.
Are you referring to the proof of the original formula of distance between a point and a line that was used?
slender gull
Distance between two parallel lines.
It does use the distance of a point from a line formula though.
silent sage
Why does the given formula necessitate the equivalence of the coefficients of x ...
Does the segment given here count as "proof"?
slender gull
Okay yeah that works.
So as you can see, the formula itself was derived assuming a and b terms to be the same.
The final result has sqrt(a^2 + b^2)
If those terms are different for parallel lines, wouldn't you wonder which a and b to use
silent sage
As such is there any other way to go about it other than converting the equation...
Right, so is there any other method?
slender gull
If you want to use the formula then there isn't.
silent sage
I suppose it will always work unless there is somehow a situation in which obtaining c for one of the lines becomes too complicated after multiplication or division.. and no point going into that unless encountered.
Thank you for your time and assistance one and all.
.close
wanton pebble
lone heartBOT
wanton pebble
is it 27?
gray isle
show work
lone heartBOT
@wanton pebble Has your question been resolved?
wanton pebble
show work
i mainly done it in head ..but x will be under 11 otherwise F(x) will be negative and we only need postive values.. so after putting all x from 1 to 10.. max value was 27
gray isle
don't do stuff in your head
and if you plugged in numbers from 1-10,
you should've reached a different conclusion
and also the max value doesn't necessary occur when x is an integer
pliant kestrel
Hi
limpid spade
Hi
pliant kestrel
I have to determine r in function of p and q, complex numbers, such as when uv=u^3+v^3=r then u+v is a solution to z^3=z×p+q
Best ive come to is r+3r(u+v)=(u+v)p+q
And im unsure how i can solvz this, or if i have something that would allow me to say r=q and 3r=p for example
(This is part of an assignment that aims to find a general solution to 3d degree equations)
Does anyone have a lead ?
lone heartBOT
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pliant kestrel
.close
lone heartBOT
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slender pilot
how do you get the population rate for 15,069 and 16,136 because I tried getting the rate using the equation P=P2-P1/P1x100 and in gave me 7.08 then I used my exponential growth equation to check if I'm right then I got 16,135 the equation was P=15069(1+0.07080)^1 so I'm asking if my rate is right
alpine sable
not sure what the question is
sorry, I get what your saying but I could help if I saw the question written out. Thanks
mortal trellis
are you asking why you got 16135 instead of 16136?
you rounded to get 7.08
it should be 7.08076..... etc
so that small rounding error means you are off by 1
slender pilot
here's my table
if I did not round it off the percent will be different
I cannot find any similar percent that could lead to the following numbers if I use the exponential growth rate
mortal trellis
ok I don't understand your question. 7.08 is correct (up to rounding)
slender pilot
because after we found the percentage we're supposed to determine how many years it takes for the population to be 55,300
and when using the equation I came up with a new number
55,278
maybe I'm doing something wrong
oh
okay
so my groupmate just texted me
this was the equation
I was doing it all wrong
okay thank you
oh yeah
.close
somber spoke
lone heartBOT
vale wigeon
have you determined whether or not the guards are telling you the truth?
lone heartBOT
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red belfry
I've tried putting y^2 and x^2 into square root but didn't resolve it
Can someone help me out?
lone heartBOT
@red belfry Has your question been resolved?
red belfry
<@&286206848099549185>
gray isle
consider subtracting your equations
red belfry
consider subtracting your equations
Do you mean this?
(7x+2y)-(2x+7y)
gray isle
where'd the x^2,y^2 and equal sign go
red belfry
sorry, what do you mean by subtracting the equations?
keen plinth
x^2 = 7x + 2y
- (y^2 = 2x + 7y)
------------------
??? = ???
what do you get when you subtract the stuff on the left of the equals sign
gray isle
lhs_1 - lhs_2 = rhs_1 - rhs_2
keen plinth
red belfry
x^2 - y^2
gray isle
no
red belfry
Oh
keen plinth
do you know what (a + b)(a - b) gives?
keen plinth
do you notice a common factor
red belfry
(x-y)(x+y) = 5(x - y)
keen plinth
keep going
keen plinth
mhm
keen plinth
I've tried putting y^2 and x^2 into square root but didn't resolve it
now you said you tried this
what did you get
red belfry
I got sqrt(9x+9y+4)
keen plinth
can you "resolve" that now
keen plinth
simplify it
red belfry
So you checked it?
red belfry
How is called the rule we used to subtract equations?
keen plinth
hmm
im not sure if theres a name for it
its just simply the fact that
if a = b and c = d
then a - c = b - d
ocean sealBOT
keen plinth
its not prohibited
but if you start a new channel
itll get pinned
and you might get more attention
just close this one before you do so tho if you're done
red belfry
I can't thank you enough for the help
hushed whale
why( f(g(x))' = g'(x) f'(u(x))
lone heartBOT
why( f(g(x))' = g'(x) f'(u(x))
lone heartBOT
lone heartBOT
✅
lone heartBOT
@hushed whale Has your question been resolved?
blissful shale
how do u do this?
lone heartBOT
how do u do this?
lucid aurora
can i get helP>
lone heartBOT
can i get helP>
keen plinth
lone heartBOT
@lucid aurora Has your question been resolved?
lucid aurora
i still need help
gray isle
have you tried drawing a diagram
lucid aurora
i dont need help with that
A dog is travelling south in a car at 60 km/h. A cat is travelling north in a car at 40 km/h. What is the velocity of the cat relative to the dog when they pass each other?
i need help with this one
gray isle
have you tried drawing a diagram
lone heartBOT
@lucid aurora Has your question been resolved?
lone heartBOT
lone heartBOT
Available help channel!
neon lotus
Hi, so I understand that the complex numbers are written as -> z = x + iy. When my prof. says that x = Re [z] and y = Im[z], what does that mean exactly?
neon lotus
that for any value of z, x will be a real number?
mortal trellis
every complex number z can be written as z=x+iy with two real numbers x,y
x is called the real part of z, written as Re(z) and y is called the imaginary part of z, written as Im(z)
tiny cosmos
Trying to understand what an orthogonal projection means
lone heartBOT
Trying to understand what an orthogonal projection means
tiny cosmos
I just need the last bit explained to me like Im 5, orthogonal projection Pª of R onto axis a. Does this mean finding the value that axis a is contributing to R?
I think thats it actually let me calculate that
I get 962.46
without accounting for sigdigs
tiny cosmos
I wish I remembered dot product, Ill go through this and see if it gives me any trouble
thank you
@tacit arch if youre too busy thats fine, but do you also get 962.46? I think I was right when I said its just what the projecting vector contributes to the vector we like
ocean sealBOT
Result:
0.70710678118655
ocean sealBOT
Result:
171.42580631807
Result:
0.85090352453412
oh its in radians
fair osprey
lone heartBOT
tacit arch
do you know how to flip inequalities when negating? like $x < y$ implies $-y < -x$
ocean sealBOT
riemann (eric tao for honorable)
fair osprey
so it'd be -2.2+5 and -2.3+5?
tacit arch
**riemann (eric tao for honorable)**
write your statement in full inequalities like this
fair osprey
2.7 < 3-sqrt(5) < 2.8?
tacit arch
2.7 < 3-sqrt(5) < 2.8?
no. can't help if you don't show full work how you got there
fair osprey
??
tacit arch
2.7 < 3-sqrt(5) < 2.8?
i mean how did you get this
explain with words or show the full steps
fair osprey
making the 2.2 and 2.3 negative then adding 5?
tacit arch
making the 2.2 and 2.3 negative then adding 5?
why are you adding 5?
5 - sqrt(5) is not the same as 3 - sqrt(5)
fair osprey
Oh wait wrong number
so add 3?
that worked
also how do i find the domain os this?
lone heartBOT
@fair osprey Has your question been resolved?
royal meadow
@fair osprey you can't take the square root of a negative number, so the domain will be all the numbers where neither of the roots have to deal with something negative
ie. 3 - 2x >= 0 and also 1 - x >= 0
lone flower
He's wrong
ancient meteor
So you can take a square of 0?
Well you can take square of any number
If you meant square root then yea you can only take it for positives and 0
ancient meteor
Yes
fair osprey
also for this, what does roots smean?
echo socket
Another term for solutions to an equation
swift shore
Yep
white garnet
Hey guys, can someone that is insane at math help with this one?
I have this formula for trajectory and what I know is point in 0;0 and point in 6;3 and initial velocity v=10.
How do I solve for angle?
tacit arch
is v constant or a function of time?
white garnet
constant, it's inital velocity
tacit arch
what equation do you get for point (6,3) ?
white garnet
imagine I know from where I am thowing and where I want for example ball to land, so I know 2 points, I also know velocity of the throw so I need to find the angle I need to throw at
I am sorry if it isn't clear what I want
tacit arch
i mean plug in (6,3) here
white garnet
yeah, but I need "universal" solution so I can reuse it in a code for a game
basicly theta on one side and all other variables on other side
tough jasper
Oh interesting
tacit arch
yeah, but I need "universal" solution so I can reuse it in a code for a game
did you try algebra?
and definition of tangent / pythagorean identity
white garnet
slow down a bit, I am not that good at math
what I tried was wolfram alpha and lot's of paper for solving like a system of equations but it didn't work out
tacit arch
$\tan(\theta) = \frac{\sin(\theta)}{\cos(\theta)}$
ocean sealBOT
riemann (eric tao for honorable)
ocean sealBOT
riemann (eric tao for honorable)
white garnet
This might be helpful. Thanks for know and I will come back tomorrow. Need to get some sleep.
tacit arch
.close to free up the channel
white garnet
.close
timid wind
what is it
lone heartBOT
what is it
timid wind
also please explain it to me i dont just want the answer
weary wyvern
what is it
For a) write n = 2k + 1 for some integer k to use the fact that n is odd
timid wind
For a) write n = 2k + 1 for some integer k to use the fact that n is odd
but how can i use that to prove it is divisible by 3
like i cant just give an example
weary wyvern
Use it how
weary wyvern
can i use the expression (2^2k+1)/3
Yes but what's your idea after this?
weary wyvern
Alright then do what I said
timid wind
can you give me an example
heady pollen
just out of curiosity, you haven't covered induction, have you?
timid wind
nope
heady pollen
there is probably an easier way than using induction, but in case you want to know:
we start by proving the expression for the smallest k, here k=0
then we want to prove the expression for k+1, here we can use the fact that we already proved it for k
timid wind
when they mean disible by is it 2^n+1/3 or the other way around
timid wind
there is probably an easier way than using induction, but in case you want to kn...
would you know any easier way?
heady pollen
sadly no
this is my take
this is the best i can do for an explanation
i know it is not the best, but it is hard to describe
we prove the expression for some a and the following.
the key is that we prove it generally, without substituting in any numbers.
now we can interpret the second a, for which the expression is proven.
by the logic of step one, the following is already proven.
this carries on and on to prove for every possible a
but since you have not covered it, i doubt that is what you should do
i will think a bit about a different way
lone heartBOT
@timid wind Has your question been resolved?
pallid scarab
but long story short, you can write (3-1)^n = 3*[3^(n-1) + ...] + (-1)^n = 3[...] - 1
atomic cloak
hi
lone heartBOT
@timid wind Has your question been resolved?
timid wind
<@&286206848099549185> , sry for ping but it has been 30 minutes
tacit arch
try working in modulo 3
tacit arch
they're all divisible by a small positive integer
timid wind
how am i suppose to use that to prove it
alpine sable
if p is a prime then it is not divisible by 3
however, p+1 or p-1 will be
therefore (p+1)(p-1) will also be divisible by 3
which equals p^2-1
p^2+2 is p^2-1, and if p^2-1 is already divisible by 3, then p^2+2 will be too given that it is (p^2-1) +3
therefore p^2+2 is a composite number
tacit arch
therefore p^2+2 is a composite number
try not to do entire problems for them
lone heartBOT
@timid wind Has your question been resolved?
lone heartBOT
@timid wind Has your question been resolved?
flat edge
How do I determine the common ratio of the geometric sequence given the pair of terms
prime badge
second divide by first
ancient meteor
Since a9 and a10 are consecutive terms in the progression, you know that r*a9 = a10
flat edge
But how will I divide fractions?
prime badge
u can google how to divide fractions
flat edge
Wait what
prime badge
just reading the screenshot 🤷♂️
flat edge
So u divide the then subtract 3/5?
flat edge
just reading the screenshot 🤷♂️
Oh crap my bad I didn’t notice the negative sign
So I cross multiplied them and got -15/-30
And I simplify and got -1/-2 is that correct?
prime badge
the minus is for the 3
flat edge
So like -15/30 would’ve been how it looked like
prime badge
(3*5)/(10*−3)
flat edge
So 15/-30?
prime badge
either one is correct
flat edge
And simplify it so it’s 1/-2?
prime badge
or-1/2
flat edge
And that’s the answer?
prime badge
yea
flat edge
Alright thank you so much
lone heartBOT
@flat edge Has your question been resolved?
edgy sand
lone heartBOT
thick flame
hey guys, what would i use to solve this?
The reduction formula.
keen plinth
noooo not reduction formula
that's only when you only have even powers of sin and cos
and you have no other choice
this one is just a substitution
edgy sand
okay thank you
ornate condor
did someone say
edgy sand
u sub is fine right?
ornate condor
❤️
wanton tusk
❤️
ornate condor
u can literally
keen plinth
make sure you find the correct u sub
ornate condor
as long as the variable is not already being used
edgy sand
oh yea which one would I be subbing? the sin or cos?
like how can I know which one to do in this case
keen plinth
because that'll be used as the derivative
edgy sand
okay so the sin then gotcha
keen plinth
the idea is
you can rewrite the even powers of cos
as sin^2
and you get 1 power of cos left over
to use for the derivative
so you u sub the sin
edgy sand
ahh ye that makes it easier
keen plinth
and the cos will be there for you
edgy sand
makes sense, thanks
keen plinth
cool cool
edgy sand
.close
thin urchin
lone heartBOT
ocean sealBOT
riemann
tacit arch
did you input 2 in the wrong box
thin urchin
tacit arch
