Homework Statement
Below is the bode plot of return difference, 1+C(S)P(S) in a feedback system. Identify the frequencies where the feedback is large, negative, positive and negligible.
P(S) = \frac{100}{s^2+2s+1}
C(S) = \frac{220(s+50)}{s+200}
Homework Equations
Bode Plot, Feedback
The...
Homework Statement
The state space model of a nonlinear system is
x'_1(t) = 2x^2_2(t) - 50
x'_2(t) = -x_1(t) - 3x_2(t) + u(t)
Where x_1(t) and x_2(t) are the states, and u(t) is the input. The output of the system is x_2(t).
Find the state space model of this system linearized at the...
Yeah, translating the axes by defining a new set of axes such as x' and y', then rotating it via trigonometric function but I was struggling big time about that. Any suggestions?
Homework Statement
Come up with a set of equations to draw the following picture:
http://img197.imageshack.us/img197/7428/equation.jpg [Broken]
Homework Equations
The Attempt at a Solution
The circle is easy.
1000 = sqrt(x^2+y^2)
I can just model the equation with sines. So
y_1 = 300...
Homework Statement
Let the independent random variables X1,X2,X3 have the same cdf F(x). Let Y be the middle value of X1,X2,X3. Determine the cdf of Y.
Homework Equations
F(x) = P(X<=x) = ∫-inf to x f(y)dy
The Attempt at a Solution
I don't understand the question, what does it...
Homework Statement
A gas supply company is trying to set up contracts with two clients, A and B. The company will make a profit of ten million dollars for each contract that is successfully agreed. The probability of agreeing a deal with client A is 1/4 and the probability of agreeing a deal...
I know this probably isn't the best place to ask this question but here goes anyways lol
What's wrong with the next sentence/
"What do you feel when you see a smoke detector? Do you ever feel like an astronaut? No? Well, the next time you see one, try to imagine that it's part of your...
The class is known as Advanced Discrete Structures, crosslisted with Mathematics and Computer Science. Apparently we cover topics of both formal logic and abstract computer science.
This is the notes we got from the professor. Maybe this would be of help...
Homework Statement
Prove by finite list induction
∀xs:: [a]. map (\x -> x) xs = xs
Homework Equations
map f [ ] = [ ]
map f (x : xs) = (f x) : map f xs
The Attempt at a Solution
The list induction principle to prove a finite lists of type a is
[P([ ])^
∀x :: a. ∀xs ...
Homework Statement
1. f(n) = log(n) ^ (log(n)). Simplify for Big-O notation.
The Attempt at a Solution
1.
I'm just trying to prove a big-O notation for one of my courses, and this was simplified to
f(n) = n^log(log(n))
And I'm having a hard time seeing why. Any guidance would be...
Homework Statement
Problem 1:
Two Arithmetic Sequences are given.
a_n = 200,196,192,188,184...
[ltaex]b_n = 100,103,106,109,112...[/itex]
For integers l,m, find the number of pairs consisting of (l,m) which satifies condition a_l = b_m
Problem 2:
Three terms, sin(x)...
Homework Statement
x^4 + 3x^3 - 7x^2 - 15x + 18 = 0
Find x
Homework Equations
First Derivative?
Second Derivative?
The Attempt at a Solution
Normally, I'd use Ferrari's method to tackle this problem but I am required to use derivation to find the answer...
Where do I go from here? Do...
Homework Statement
Find the limit of
\frac{x^3-2x^2-9}{x^2-2x-3}
as x->3
Homework Equations
The Attempt at a Solution
You factor the bottom portion and top portion, then it looks something like this
\frac{x(x^2-2x)-9}{(x-3)(x+1)}
I feel like I can go further about eliminating the...
Just so that I understand, why is it that the cylindrical shell method must be applied here? I was taught that when finding a volume revolved around X or Y axis, the above equation works well except you just have to be careful when you plug in for X or Y.
Homework Statement
The region bounded by y=e^-x^2, y=0, x=0 and x=1 is revolved around the y-axis. Find the volume.
Homework Equations
V = \int_{a}^{b} R^2 dy
The Attempt at a Solution
We must first express x in terms of y. So we get
\ln y = -x^2
x^2 = -\ln y
We substitute this to the...
Homework Statement
1.
f(n) = n - 100
g(n) = n - 200
2.
f(n) = log(2n)
g(n) = log(3n)
n >= 0 in all cases
Find out if f(n) is an upperbound, lowerbound or both of g(n)
Homework Equations
The Attempt at a Solution
in case of 1, f(n) has to be an upperbound of g(n) because...
U( r ) = r(r+1)(r+2)(r+3), show that U (r + 1) - U ( r ) = 4(r+1)(r+2)(r+3)
U(r+1) is = (r+1)(r+2)(r+3)(r+4)
so U(r+1) - U( r ) = (r+1)(r+2)(r+3)(r+4) - r(r+1)(r+2)(r+3)
let (r+1)(r+2)(r+3) = z
= z((r+4)-r)
= 4z
= 4(r+1)(r+2)(r+3)
Then if we say V(r) = U(r+1) - U( r )
V(r) + V(r + 1) =...
Homework Statement
U( r ) = r(r+1)(r+2)(r+3), show that U (r + 1) - U ( r ) = 4(r+1)(r+2)(r+3) Hence, find the sum to n terms of the series 2x3x4 + 3x4x5 + 4x5x6 +...
Homework Equations
Sequence Knowledge..
The Attempt at a Solution
I can't even TOUCH on the problem. Can you...
Homework Statement
http://img24.imageshack.us/img24/9028/72841137.jpg [Broken]
Homework Equations
Routh-Hurwitz Stability Criterion
The Attempt at a Solution
For first question, you just write the Routh Array, make sure that the first row is all positive and you get Kmax = 1. Simple enough...
Homework Statement
Show that the first three non-zero terms in the series expansion of (1-1/n)^1/n in ascending powers of 1/n are 1-(1/n)^2-1/2(1-n)^3 and find the term in (1/n)^4
Homework Equations
Macclaurin? Taylor?
The Attempt at a Solution
Can someone please point me on...
Homework Statement
If P is proportional to q^2
and q is inversely proportional to r
Show that p is proportional to r^2
Homework Equations
p = kq^2
q = c/r
where k and c are proportional constants
The Attempt at a Solution
I'd say this is impossible. This is all the...
I thank you for your reply, but that is exactly what I was trying to avoid. This problem was shown on 6th grade exam paper, and should not require any trigonometry to solve this. Are you absolutely certain that is the only way to go about this problem?
Homework Statement
http://img16.imageshack.us/img16/9616/area.jpg [Broken]
The Attempt at a Solution
Area of square = 25cm^2 therefore
Area of the shaded area = 25 - (Area of A + Area of B + Area of C)
Area of A = Area of C
Therefore, Area of the shaded area = 25 - (2 * Area of...
Well, here's the whole problem:
The two exponential functions
f(x)=a^{bx-1}
g(x)=a^{1-bx}
Satisfy the following conditions
a)Functions y = f(x) and y=g(x) are symmetric to the line x = 2 when graphed
b)f(4) + g(4) = \frac {5}{2}
Find a and b.
Homework Statement
Suppose two exponential functions, f(x) and g(x) are symmetric with respect to x = 2.
f(x)=a^{bx-1}
g(x)=a^{1-bx}
Prove f(2) = g(2)
Homework Equations
The Attempt at a Solution
This isn't actually a problem. This is a property used to solve a different...
Then that simply means
f(b-1) = 1
f(b+1) = 1
So we have
1 = (b-1)^2 - 4(b-1) + a
1 = (b+1)^2 - 4(b+1) + a
0 = (b-1)^2 - 4(b-1) - (b+1)^2 + 4(b+1)
0 = (b-1)^2 - (b+1)^2 + 8
b = 2
Then,
1 = (2+1)^2 - 4(2+1) + a
1 = 9 - 12+ a
a = 4
a + b = 6 is what I get, but...
I understood why the discontinuity occurs, since |x-b|^n of n to the infinity could take you to 0 or a huge value (I think it was related to geometrical sum) depending on whether it's smaller than 1 or bigger than 1. I still do not have a clue how to get the specific values of a and b from it...
Homework Statement
f(x) = x^2 - 4x + a
g(x) = \lim_{n\rightarrow\infty} \frac {2|x-b|^n + 1}{|x-b|^n + 1}
let h(x) = f(x)g(x)
Find the sum of a+b that makes h(x) continuous for all x.
Homework Equations
Power Series? Derivation to test continuity?
The Attempt at a Solution...
Ok, it's situation like these latex seriously does a commendable job of pissing me off. How would you write the summation of index starting from j = 1 until n?
Homework Statement
When a conventional apging system transmits a message, the probability that the message will be received by the pager it is sent to is p. To be confident that a message is received at least once, a system transmits the message n times.
Assuming p = 0.8, what is the...
oh ok, then the next event is {FFS] so it's (1-p)^2 * p for the third attempt.
Ok, then the total probability is p + p(1-p) + p(1-p)^2
So I set this expression equal to 0.95 and solve for p?
Ok. Obviously, the probability of getting the ticket on the first call is p.
Probability on the second one is 1-(1-p)^2 and the third one is 1-(1-p)^3
Then the total probability is p + (1-(1-p)^2) + (1-(1-p)^3)
Am I right? And from this, do I set the whole equation to 0.95 and solve for...
Homework Statement
You are a manager of ticket agency that sells concert tickets. You assume that people will call 3 times in an attempt to buy the ticket and give up. You want to make sure that you are able to serve at least 95% of the people who wants tickets. Let p be the probability that a...