# Search results

1. ### Identifying type of feedback by looking at bode plot

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...
2. ### Finding the state space model of a nonlinear system

So the evaluation at (-15,5) becomes y'= \begin{pmatrix} 0 & 20 \\ -1 & -3 \end{pmatrix} ?
3. ### Finding the state space model of a nonlinear system

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...
4. ### Drawing with trigonometric function

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?
5. ### Drawing with trigonometric function

No it can be in terms of X too. How should I modelize the lines which goes at 45 degree angle?
6. ### Drawing with trigonometric function

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...
7. ### Cumulative Distribution Function problem

Oh.. Ok I'm still a bit lost on how to tackle this problem..:confused:
8. ### Cumulative Distribution Function problem

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...
9. ### Discrete Probability Mass Function

Twenty million dollars, ten million dollars and zero dollars?? (edit)nvm I figured out ty
10. ### Discrete Probability Mass Function

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...
11. ### Random Grammar Question

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...
12. ### Induction proof on list

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...
13. ### Induction proof on list

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

Bump :(
15. ### Induction proof on list

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 ...
16. ### Really Simple Logarithmic Question

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...
17. ### Arithmetic Sequence Problem

Uh so anyone got an idea about second problem?
18. ### Arithmetic Sequence 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.
19. ### Arithmetic Sequence Problem

What.. is latex tag broken..?
20. ### Arithmetic Sequence Problem

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)...
21. ### Solving Quartic Equation using Derivative

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...
22. ### Finding limit

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...
23. ### Finding a volume bounded by a region

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.
24. ### Finding a volume bounded by a region

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...
25. ### Upper bound and lower bound

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...
26. ### Arc Tangent Squared

so [arctan(3)]^2 = arctan(3) * arctan(3) ?
27. ### Arc Tangent Squared

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??
28. ### Sequence Question

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) =...
29. ### Sequence Question

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...
30. ### Feedback Control Systems

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...
31. ### Ascending powers math help

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...
32. ### Proportionality Question

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...
33. ### Finding sector area

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?
34. ### Finding sector area

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...
35. ### Symmetricity of exponential graphs

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.
36. ### Symmetricity of exponential graphs

Something is wrong, the answer is supposed to be a+b = 1 though
37. ### Symmetricity of exponential graphs

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.
38. ### Symmetricity of exponential graphs

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...
39. ### Continuity of the function

 Oh, it's actually f(b-1) = 0 f(b+1) = 0 Doh! Thx
40. ### Continuity of the function

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...
41. ### Continuity of the function

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...
42. ### Continuity of the function

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...
43. ### Find the coefficient of static friction help?

You need the mass of the object at the least to solve the problem. Otherwise, this is an impossible problem.
44. ### Minimum value Probability Question

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?
45. ### Minimum value Probability Question

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...
46. ### Probability Mass Function

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.
47. ### Probability Mass Function

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?
48. ### Probability Mass Function

Probability of failing the first time is 1-p
49. ### Probability Mass Function

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...
50. ### Probability Mass Function

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...