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secret--
hint: ||asia||
well, next time i think you should consider other solutions in case they're simpler
yeah aas is the only thing i could see there
since vertically opposite angles are equal
Yeah, totally.. It takes less energy too
Thanks ,guys
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how do i get the range for this function
y= x^2-1/x+1
$y = x^2 - \frac1x + 1$?
ℝamonov
Roberttt
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Roberttt
you should use parentheses to clearly indicate the numerators and denominators
what's the range for a straight (non-horizontal) line
also consider where this expression is undefined
do you know what the definition of range is
u mean straight vertical line?
i mean what i said
yes i just didnt see what u were saying
y>0
?
OH wait nvm
sorry
all real numbers correct?
yes. though for this you would also need to
also consider where this expression is undefined
so all real numbers and y cannot = -1?
cuz this says the range is -2 and i am very confused
note that y = (x^2-1)/(x+1) → y = x-1 except for when x=-1
where it would be undefined
so there is a hole>?
yes
x^2 - 1 is a difference of two squares
-2
i see
ok
so range is all real numbers and y cannot = -1
and hole is at (-1,-2)
@livid hound yes?
no
you're confusing domain with range
OH nvm
i see
cuz
-2
is undefined
so all real numbers and y cannot = -2
now im right?
yeh
they can be at different locations
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why the particle is speeding up only when velocity and acceleration have the same sign
its a pretty basic question but cna someone explain it pls
Sign means same direction
Acceleration doesn’t mean necessarily increase of speed. If you are driving and you are accelerate in the opposite direction, then you are are slowing down
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can anyone help me with this? im unfamiliar with that form of derivative
does that just mean doing it twice? or
yeah
just take the derivative twice
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a
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✅
hi
can someone create a word problem of this given picture involving angle of elevation or angle of depression.
i'll solve it
@granite holly Has your question been resolved?
what did the question ask for?
angle A , B , C?
if so then all the angles should be equal because its is an equilateral triangle as all sides are 88m
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Hi I was looking to get some advice. I have a convex compact subset E of a normed vector space X with a strictly convex norm and I want to show that there exists a smallest norm in E, $\lVert x \rVert<\lVert y \rVert$ for all y in $E-{x}$. Any advice would be appreciated.
Cleetus-Wazoo
I tried using the parallelogram law and Cauchy sequences to show existence, but later recognized that I couldn't use it since we don't have an inner product. After that attempt I've been really stuck on how to show existence.
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i have N(90,13) probability , that's demand for 30 days. what is the probability for 1 day?
ping me
You make a word problem
Like there are 3 flags one in the left 2 in the right
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@naive yew Has your question been resolved?
Missing context - wdym with demand for 30 days? Wdym with prob for 1 day?
Post full question
that's the full question.
demand for item varies with normal probability of N(90,13)
i want the daily demand
“Demand for item varies” over what period? Before you said prob for 1 day now say daily demand
Copy-paste the exact wording
Don’t just pick random parts of it and post
lol first is demand for 30 days
i need demand for 1 day
so split this probability ?
i think N(90/30,13/30) am i right?
Not a probability
whatever the name of N(90,30) is to you. english is not my first language
Doesn’t work like that on variance
probability , equation
Its a distribution
yeah
.
can i split it or not?
give me more clues? lol
i don't get you
this shows exactly what i did
No if X is normally distributed with mean 90 and variance 13
You want to find distribution of Y=1/30 * X
So there is no sum law here
can you link me to how to solve it
and the E is 90/30 regardless, right?
Why don’t you check expected value properties while you are at it then if unsure
But try googling normal distribution multiplied by constant for example
If you don’t wanna look in your book
look, it's a class that is not related to statistics. i studied statistics long time ago, but i need this calculation. can you please help me? or talk in riddles?
i don't have a stats book to look at
i need help otherwise i wouldn't ask for it
Is giving you exactly what to google talking in riddels?
Like what
and endlighs is not my first language like i told you, so definitions varies in my language
i googled "varicance law"
don't know what to pick
You trolling?
Google this click any link you get
And I guarantee answer is there no matter what you click on
Bruh
i said i didn't notice
now i did
so is it sqrt(13) lol @elfin hemlock
no
judging by that
the distribution for 1 day is the same for 30 days ?
?
Google “constant multiplied by normal distribution”
Click any link - for example this
https://math.stackexchange.com/questions/1923924/normal-variables-adding-and-multiplying-by-constant
Read top answer
X1 - N(90,13), X2 - N(90,13), X3 - N(90,13).... X30 - N(90,13) probability for each day, for 30 days
if i sum them up i will get X - N(90,13)
maybe this is nonsense
checking your link
thank you @elfin hemlock for your help
Np teaching you how to google
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For what values of m is (m-2)x + (m+2) ≥ 0?
No idea how to go about doing this; was absent
To be exact this is the question, I assumed that you'd have to divide it into two cases: quadratic (kwadratowa) and linear (liniowa), and take their union; the former I have solved, with the latter I struggle
It begins at '51, 52 Dom 243'
I don't understand what are you really trying to solve? 
So since the question asks for which values of m is the domain of f(x) is real, I wrote Warunek 1 (Condition) that what's under the root must be greater than 0
Do you understand now?
yea 
Is this supposition correct?
I don't know, I would just do mx^2+(m-2)x+(m+2) > 0 
Not ≥?
How would you solve it
Let me compare your method with mine and learn this way
Since mine has confused you
So what I think I would do is use the formula to find the x coordinate of the vertex of the parabola and set that ≥0
But also a>0 so that the parabola is facing upwards
Yeah, it has to be facing upwards, since f(x) ≥ 0
But I'm not sure how would you go about doing what you have described
I have only shown that if we are considering a quadratic, then m > -2 + 4sqrt(3)/3
Actually
I suppose if the function is linear then m is equal to 0
Then we have -2x + 2 ≥ 0
But does it have any relevance or is the above enough
Since
y coordinate of course, not x
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Any chance someone can help me with this linear equation system. The only known factors are G, mü(0) and Alpha
I know for a fact the answer to the question managed to get rid of N
But I seem incapable of doing that
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i need help, is that true that i use the true method for those question?
wdym? i'm new here actually and dont know how to get help
Only post in channels marked available.
When a channel opens you gotta type in it to occupy it
Only the ones with no names in them are open if they have usernames in them they are occupied so don’t do it in those
oh i see, thank you
Np
Ok @blazing blade I'm thinking define the integral in a different way, so divide A = [0,1]x[0,1] in such a way that x^2 \leq y^2 in one part and y^2 \leq x^2 in the other part
wait, how to know its already have name or no name?
After the help 13 if it has any other words in it it’s occupied
The discord sorts out the channels by available and occupied I believe
its available
This def works for the function max{x,y} since you divide along the diagonal, but I'm still thinking about how to for max{x^2,y^2}
i see, thank youu
I'm pretty sure that the line of division is the same for the squared case since we're in a nonegative range for x and y
so define your integral as $\int_{A'}e^xdydy + \int_{A''}e^ydydx$ where $A' = {(x,y) \in [0,1]^2 | x\leq y}$ and $A''$ is defined similarly
glittersparkles
Ahhh A' is for y\leq x
A'' x \leq y so max{x,y} = y
@blazing blade I hope that helps 🙂
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Hello! I am interested in finding the eigenvectors of a matrix containing NA values in R, but I am not sure how to handle the NA values
It's been a while since I took linear algebra
@tired hull Has your question been resolved?
<@&286206848099549185>
I think I may be thinking about my matrix incorrectly
One sec
"where A is the matrix with entries a_ij/n_i."
I am not sure how to interpret that sentence.
The paper I'm reading can be found here:
http://stat.wharton.upenn.edu/~steele/Courses/956/Ranking/RankingFootballSIAM93.pdf
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how do i graph transformations of cotangent
gotta be more specific than that
how would i graph 3cot(1/3x+pi/2)-2
i can do the vertical shift, and the period, but i dont understand how to calculate the horizontal shift
horizontal shift is within the parenthesis there
wait is it b/-c
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Im trying to integrate normal distrubution function but I am stuck at the limit part
I found infinity but it is supposed to be 1
the interchange of the sum and integral signs was invalid
the integrals of each summand diverge
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okk
the r or some shit
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How do i calculate the surface?
@round turtle Has your question been resolved?
uh
what is pi in this situation
the surface of what tho?
if it's the semi-circle then
Area = πr^2/2 = πd^2/8
r is the radius, d is the diameter
It's not a semi circle, the 10√3 is not the diameter
Yea sorry I should've made it clear when i asked my question
No its less than a half
Thanks
ask it in #help-0
is the altitude starting at the midpoint of the line?
No it isnt
What i thought about doing is drawing a triangle inside the circle
i'm doing that as well
same
It isnt??
I dont think we can solve it then
If it passes through the midpoint then we can determine some angles
true
it's not either
What's the surface if the altitude starts at the midpoint of the 10√3 line
just angles bro
Yea you need angles and you can use some tricks
how how how
Lemme draw
And then since its iscosceles and one angle is 60°
Its a whole equilateral triangle of side 10√3
.
.
Lol
Frix rephrased their question
If it isnt at midpoint then
impossible
Exactly
So what's the solution if the altitude is in the midpoint of the line
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So? Any help?
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<@&286206848099549185>
do you know how to start?
not really
yep
it'll get worse before it gets better 😅
you'll have to FOIL it, can't distribute the quadratic
but yes eventually you expand
so would it be 9x2=5(x2 +4x +4?
yep!
cool
now solve for x
no im tryna reaarange to get in the form of a +b root 5
yep!
i have ended up at x2-5x-5
cool 😎
then you get to pick how to solve that quadratic
since we're expecting sqrt 5 to come out, prob just easiest to use quad formula
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no worries!
@pseudo shale one thing before you go! make sure to check for extraneous solutions (since we squared both sides, we kind of lost info on what is negative)
ye i got it
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An event happens 10 times/hour on average
Said event has a 90% chance of bringing you 100 points
And a 10% chance of bringing you 2000 points
How do calculate the average number of points gained/hour?
find the number of times it would bring you 100 points per hour (times 100)
add it to the number of times it would bring you 2000 points per hour (times 2000)
Do you mean like this: (0.9 * 100 * 10) + (0.1 *2000 * 10) = 2900 points/hour?
In other words, 9 times per hour you get 100 points, and 1 time per hour you get 2000
2900 points per hour
On average, anyway
Ok, is this the case even tho the event only happens 10 times on average?
Not guaranteed to be exactly 10/h
Right. We are talking averages, after all
Not guaranteed to be exactly 2900 points/h
For example, for any given hour, you could hit the 2000 twice, or never.
Ok, now let’s say that after one hour, however many points I get I take them ^0.2 and that’s how many $ I make. Is 2900^0.2 the average amount of $ I will make?
Yes
Ok, now, if I want to take the distribution of $ gained into account, how do I do that?
(This is the last question lol)
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Usually, people would want to convert degrees to radians, or, more generally, convert numbers from the interval [0,360] to the interval [0, 2pi]. However, I would like to convert numbers from an interval [0,360] to (0,2pi) instead.
How should I go about this?
In more abstract (and more general) terms, find a linear transformation from [a,b] to (c,d).
oh, also, i'll probably be offline soon
$$\text{value in degrees} * \frac{\pi}{180} = \text{value in rads}$$
dldh06
Is that what you mean?
can you... uh, read the question again?
i wanted to convert it to a number in (0, 2pi)
not [0,2pi]
That is a value in (0, 2pi) though
Do you want 0 and 2pi to be not included? If so can you use limits?
yesh
well
that's that i want
(i mean, i can create a bijection between those, but since i want to convert angles, it has to be a linear transformation as well)
(which i don't know how to create, apparently)
excuse me but who pressed that? My question was not resolved
what would 0 degrees correspond to if I were to use limits?
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If you read the message after, it says the channel got close because it timed out
Oh I see how it works now sorry for interrupting, idk why, but didn't get a sound notification for the ping
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could someone give me a hand with a tiny little section of pde
I'm trying to understand how to determine the eigenvalues in 2d polar laplace with 2pi periodic boundary conditions
it always seems to end up circular
how do you get natural numbers out?
we should have that $\Theta(\pi) = \Theta (- \pi)$ and $\Theta ' (\pi) = \Theta ' (- \pi)$ right
jan Niku
it doesnt seem to help you determine eigenvalues though
since both theta and theta prime are going to be the same at any two points separated by 2 pi
im trying to track pages like this https://math.libretexts.org/Bookshelves/Differential_Equations/Book%3A_Elementary_Differential_Equations_with_Boundary_Value_Problems_(Trench)/11%3A_Boundary_Value_Problems_and_Fourier_Expansions/11.01%3A_Eigenvalue_Problems_for_y''__%CE%BBy_%3D_0
but its really just two uhh
im having a hard time tracking it
<@&286206848099549185>
@violet flume Has your question been resolved?
i'd try your luck in #odes-and-pdes
its an unlucky channel lol
😦
@violet flume Has your question been resolved?
@violet flume since this is eigen stuff, you can probably ask in #linear-algebra
actually wait no
im not sure its a fully meshed context
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would this represent charge Q at time t?
∫ I(t) dt = ∫ Q'(t) dt
meaning change in current I? from t=a to t=b?
Have you seen the second fundamental theorem of calculus?
Or, have you carried out many integrals in the past?
Basically,
∫ Q'(t) dt = Q(b) - Q(a)
im new to integrals, i learned the second theorem last week
Which is the change in charge, between time b and time a
right
charge Q ok
sorry got confused there thanks💯
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i have this function:
would calculating the derivative help me with this? cause i did that but don't know what now
you want to maximize the slope of the tangent
the derivative is the tangent line. you want to find the point where the first derivative is greatest
so (correct me if I'm wrong) you need to find the second derivative
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tes
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i did not mean to make all of those
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<@&286206848099549185>
I cannot find the root sqare for 46,352,529
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6808.2691633
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$-\frac{2x}{3\left(1-x^2\right)^{\frac{2}{3}}}$
doggo
this is what I got for the second derivative
and I got +-1 for the critical points
and using the second derivative test, I get undefined
does that mean there is no local maxima and minima?
<@&286206848099549185>
<@&286206848099549185>
@crimson sedge Has your question been resolved?
@crimson sedge Has your question been resolved?
<@&286206848099549185>
My calculus is shaky but I would still like to help however I can. Do you still need help right now?
@crimson sedge Has your question been resolved?
@crimson sedge I think you forgot to include 0 as your critical point (plugging in x = 0 into your second derivative will equal zero)
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hi, i have one conclusion is f''(x) = 0 at some point in the interval [-1,1], what is another conclusion?
by rolles theorem^
@hazy rover Has your question been resolved?
that one is true don't know about others
@hazy rover Has your question been resolved?
The other one might be that f'' is bounded ||since it is continuous on a segment||
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During the rainy season the water level in a certain lake rises. A road already exists
through the school that goes over a circular lake. The local government wants to build
another road through the school that connects to this road but not go through the lake.
The city engineer can measure the road that already exists, and he finds that the bridge
portion of the road is 5 kilometers, and the portion of the road from the bridge to where
the new road will be is 4 km. How long the road will be constructed. (Hint: Use tangent
line).
the question is REALLY unclear
Yeah thought so too
extra extra emphasis on R E A L L Y
I can't even draw a proper illustration
did you translate this from another language?
@uneven terrace Has your question been resolved?
Nope this is the question
I think our school's probably high
I solved it using secant tangent theorem
This is probably okay.
Thanks for the time tho
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$\sqrt{1+\sqrt{2+\sqrt{3+\sqrt{4+\sqrt{5 ...}}}}}$
EndTimes
show increasing and bounded
is it bounded?
yes
i mean just numerically speaking it does seem to converge
but analytically speaking idk where to start
would it be fruitful to consider this series:
$n^{\frac{1}{2^n}}$
EndTimes
1^(1/2), 2^(1/4), 3^(1/8), ...
because that's approximately how much it grows each time?
huh
huh?
.
but how?
induction or continuous application of a simple inequality works
yeah idk how you're supposed to use induction on this
there's no closed form for the series
I'm looking at a sequence like I have said
what do you compare it to
can show sqrt(k+sqrt(k+1+...)) for k>=2 is bounded by 2k hence sqrt(2+sqrt(3+..)) is bounded by 4 hence sqrt(1+sqrt(2+...)) is bounded by sqrt(5)
@bold hinge Has your question been resolved?
can show sqrt(k+sqrt(k+1+...)) for k>=2 is bounded by 2k
would you mind explaining how to do this
it's not at all obvious to me
you're still omitting a lot of details
feels like you are doing so intentionally to be uncooperative on purpose
again you aren't the one asking for help
so what
maybe i am curious about this too
independently of the help-seeker
let $a_k = \sqrt{k+\sqrt{(k+1)+\dots}}$
assuming for granted that $a_k$ exists at all, we might get $a_k = \sqrt{k + a_{k+1}}$ but it's not clear to me whether or not this recurrence relation is actually something we can use
Kanga Gang Annihilator Ann
do the induction on the length of the nested radical. sqrt(k)<2k is obv true. For induction step you then have sqrt(k+Q), where Q is a nested radical of length n-1 so use induction hypothesis on that
hence sqrt(k+Q)<sqrt(k+2k+2)=sqrt(3k+2)<2k
wait what? i thought you were dealing with a sequence of infinite nested radicals to begin with.
now we have a increasing and bounded sequence
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✅
let $a_k = \sqrt{k+\sqrt{(k+1)+\dots}}$ where $k \geq 2$, then $a_k \leq 2k$.
is this or is this not what you want to claim here? @elfin hemlock
please just answer my yes/no question i'm begging you
Kanga Gang Annihilator Ann
a_n not a_k. We are showing a_n is bounded by induction (like I showed above).
Hence our series can be viewed as a increasing and bounded sequence
Hence limit exists
what difference does it make which index i use?
a_n denotes the length
Has nothing to do with the k in the sequence definition
a_1=sqrt(k)
a_2=sqrt(k+sqrt(k+1))
@bold hinge Has your question been resolved?
k=2 in our case obv just a stronger result proven
What’s a_n in terms of a_(n-1)?
Looks pretty nasty. Should let k be a parameter and use double induction
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The function $f$ satisfies
[f(\sqrt{x + 1}) = \frac{1}{x}]for all $x \ge -1,$ $x\neq 0.$ Find $f(2)$.
d-static
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Let
[f(x) = \frac{3x - 7}{x + 1}.]Find the domain of $f$. Give your answer using interval notation.
is the answer
d-static
$(-\infty, -1) \cup (-1, \infty)$
d-static
is this your answer?
doman of $f$
d-static
yes, your answer is correct.
ok
thank you
Let
[f(x) = \frac{3x - 7}{x + 1}.]Find the range of $f$. Give your answer in interval notation.
d-static
how do i find range again?
Try to see what kind of graph is this
is it parabola?
no
hmmm
i know that i have to set some things equal to each other
how can i find the range
is the answer $(-\infty, 3) \cup (3, \infty)$?
static
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0 is an inflection point not a critical point
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guys i just dont understand this please i just need helo
<@&286206848099549185>
sorry i saw this now il show you the qs
yeah i have the truth table
but when im trying to do them i get complex
its not an easy circuit
yeah i know its so difficult for me
maybe try to label the gates in a way that it's easy for you to quickly know what they mean
for an and gate for example you maybe can label it "both"
maybe that will help 😄
yeah i have to label them lol like
you there
With only two variables it'd be pretty easy to just brute force
As long as you know the function of the gates
thats where the trouble is as far as i've understood
Oh
all the gates together make it difficult for them to figure out what happens
I mean you just gotta do it one step at a time
i got notes on the function gates but i dont know where to strart first
no i dont please help me
Their names are pretty sensical imo
Do you know the basics of boolean stuff
Like 0's and 1's
False and true
yeah a bit
alright
So the three basic gates take in 1s and 0s and give out 1s and 0s
Based on certain conditions
First you should write all the possible combinations for two inputs
So the and takes in two inputs
If the first one AND the second one are 1 or true
It gives out a 1 or true
Does that make sense
Because it's an and gate
im starting to get it a bit can i do them and show you after please
So for example 1 AND 0 would give out 0
Because they're not both 1
1 AND 1 would give out 1
Because they're both 1
so 0 an 1 will give me i get that let me just draw this and send it to you please sorry for the wait
Ok
Why they have drawn circles/bubble to show the wires connection?
I thought for a second that they were inverters lol
Yeah that's a bit misleading
Inverters are almost always at the base of the lead though
At least that I've seen
Yep
Far right side, are you saying it's a 1?
1 meaning on?
Because that's wrong
Flipping the switches help
Yeah try that
Because the inputs are both 0, follow the lines. If the lines are not blue, that's 0, if it's blue, that's 1
There's a big hint there
i meant 0
yeah i will but
The inputs for some of the gates are incorrect
Why are the switches label 0?
my teacher labelled them for the questions
or do i have to do the first one first which is this
Your teacher label them, to denote with one is on and off
As stated, 0 is off, 1 is on
are you talking about this one
I believe that you are confusing yourself with the labels
As I mentioned, 1 is on, 0 is off
Yes, please correct the lables
The labels you put in the circuit, some are incorrect
Like for this screenshot, the switches are blue, aka on
so that will be 1
Some of the lines are blue(on) yet you denoted them as off
ahh alright im starting to understand so the ones that are on is 1 and the ones that are of is 0#
Can you not read what I said? Blue is on or 1, white are off or 0
yeah i know now let me switch them around and show you
Do you know what the switch is in that diagram?
Circle the switch
Because it looks like you don't properly understand what a switch is when I say switch is labeled wrong
dldh06 can I ask you one question?
Depends, what is it?
Can you tell me what's Active low means?
It's bit counterintuitive, Active low is high?
Active low is basically just an inverted input
These are not/inverter gates
Active low is logic is 0
its says it beside and i think its meant for this box up here
or its for the switches
The first screenshot is telling you the possible combinations you have. If you have two inputs, an A and B, and it's binary, meaning each one has an on and off. You can have 00, 01, 10, or 11, where the first bit is A and the second is B. So if it's 00, that means both inputs are off. 10 means A is on, B is off, etc
So you can label the top switch as A, and the bottom as B, and follow the possible combinations
Ok, thanks.
But while using 74XX138 decoder which have active low output, The LED when is 0.
Why they have decided to do that way?
yeah i get that part
would the numbers be right and all i got to do is find the answers in the bottom 4
Do you wanna open a channel?
Or dm or smthn
Yep
You realize that, that table is for the circuit below that table
Oh wait never mind
You didn't find Q
Use the logic sim to find the values of Q
its for that table here il show you it
And Q is the lamp
and i need to find the q
You realize, that's all one question. The table is used to find Q, those screenshots, I believe wants you to label each line, whether it's on or off
ahhhh alright so the first one will be off but i need to label them to get the answer
ohhhh alright im gonna try do the first one and show you
is that better or nah
Some of the labels are wrong
Remember what I said? White is off or 0, and blue is on or 1
like that
Yes, better
Yes
You continue the process
which is 0 1
oh im just after understanding it il tell you when im finished the second one
is that right
ok i will tell you when im done for the third one
is this correct
So then the value of Q?
1
Yes
wait really
The light is on, is it not?
Q is the light
1 means on
So is the light on or off?
sorry are you therer
You have a label wrong
What's the value of Q?
1
1#
Yes
that was the answer
Yes
so im finished thank you very much your appreciated
so im done
Sure
sorry i meant to say am i done for that part or is there more
bro i acc know how to do it properely because of you i never it was that simple to do it was soo easy
can you help me with one more question please
Sure
Using the numbers from 0 to 9, how many 5 digit passwords can be made if the last two digits are even numbers and repeats are allowed?
I don't know anything about combinations
alright its okay thanks for helping me btw
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Using the numbers from 0 to 9, how many 5 digit passwords can be made if the last two digits are even numbers and repeats are allowed?
guys i need help on this please
0 in the front is accepted?
sorry im only seeing this now are you there
there are 10 digits, 5 of which are even
also you're allowed to repeat, so don't have to consider when certain digits have already been used
so for the first 3 digits there are 10 . 10 . 10 possibilities
and for the last 2 there are 5 . 5
so 10 . 10 . 10 . 5 . 5 possibilities, 25000 should be it
so 25000 is the answer thank you
@stiff root are you there
Not anymore
i just wanted to say your a goat fr
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Hello can somebody help me solve this question?
do you mean this?
ya
right, don't forget to multiply by r, where r is |z|
unfortunately i'm still learning complex analysis like you but i'll try to see if i can point out any of your mistakes
the max magnitude of $e^{i\theta}$ is 1, so that can't be right methinks
azeem321
i have an idea. write z = x + iy. then |e^(iz)| = |e^(ix - y)| = e^(-y) * |e^(ix)| = e^(-y)
|e^iz|=|e^(i(Re(z)+iIm(z)))|=|e^(iRe(z)) * e^(-Im(z))|=|e^(iRe(z))|*|e^(-Im(z))|.
so find a z on the circle with radius 2 that maximizes y
soap beat me :(
which in turn would minimize e^(-y)
wait, i'm being super stupid here, but how did you get |e^(ix)| to be 1
wait
r=1.
its on the unit circle
oh yeah lmao
where is this problem from?
my assignment
but yeah, |exp(iz)|=exp(-y) if z=x+iy.
i am writing this out
let me see if i understand second
how come you factored e^-y out of the modulus
ik how you factored it out of e^ix-y obviously
|xy| = |x||y|
but can u just take shit out of the modulus like that
o
so |e^(-y)|=e^(-y)
it does.
well since |z| = sqrt(x^2 + y^2)
= 2
is that how i should think of it
or in a different form
|z|=2 is a circle in the C plane.
you want to minimize exp(-y) which implies maximize y
yes
ooo
the largest Im(z) value is 2
