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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...

So the evaluation at (-15,5) becomes y'= \begin{pmatrix} 0 & 20 \\ -1 & -3 \end{pmatrix} ?

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?

No it can be in terms of X too. How should I modelize the lines which goes at 45 degree angle?

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...

Oh.. Ok I'm still a bit lost on how to tackle this problem..:confused:

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...

Twenty million dollars, ten million dollars and zero dollars?? (edit)nvm I figured out ty

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...

Did I finally break the experts here with an unsolvable question? Bump

Bump :(

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...

Uh so anyone got an idea about second problem?

I understand how you simplified the equation.. but where did you get the idea of plugging 9,19,29 for n? nvm i see it now. TY.

What.. is latex tag broken..?

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...

so [arctan(3)]^2 = arctan(3) * arctan(3) ?

Homework Statement tan(2x) - 3 cot (2x) = 0 Homework Equations Trigonometry Knowledge. The Attempt at a Solution tan(2x) - 3cot(2x) = 0 tan(2x) - 3/tan(2x) = 0 [tan(2x)]^2 - 3 = 0 [tan(2x)]^2 = 3 Is there such thing as Arc Tangent that's squared??

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...

I asked my professor and he told me that g(x) = f(4 - x), f(x) = g(4 - x), since x is symmetric to 2 Now I'm even more confused.

Something is wrong, the answer is supposed to be a+b = 1 though

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...

[Edit] Oh, it's actually f(b-1) = 0 f(b+1) = 0 Doh! Thx

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...

You need the mass of the object at the least to solve the problem. Otherwise, this is an impossible problem.

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...

Ahhhh! I should've noticed that earlier! I was like "I have to solve a third-order equation in a probability class??" haha thanks a lot.

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?

Probability of failing the first time is 1-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...