A mass on a spring is subjected to an external force that looks like a triangular wave:

F(t) = 1+t from t=-1 to 0

F(t) = 1-t from t=0 to t=1 Periodicity = 2

The differential equation for the position of the mass (using Newton’s law) ends up being: x’’(t) + 2x’(t) + 101x(t) = F(t)

1. Find the generic homogeneous solution
2. Find the Fourier series of F(t)

3. Find the Fourier series of the particular solution (which is the total solution after a long time)

4. Plot the first 5 terms of the series

knot theory

(a). what is a link? give some examples

(b) With examples explain invariants of links

We’ll say a polynomial f(x) ∈ R[x] is prime if the ideal (f(x)) ⊂ R[x] is prime. If F is a field with finitely many elements (e.g., Z/pZ), prove that f(x) ∈F [x] is prime if and only if it’s irreducible.

SYMBOLIC LOGIC QUESTION:

Recall that a valid argument is one in which it is impossible for the conclusion to be false, if the premises are true. Explain how, in this context, the Negation Introduction rule demonstrates the concept of validity.

Use a Laplace Transform technique to find the solution to the differential equation (ie. initial value problem).

y'' + 4y' + 5y = 35e^(-4t)

y(0) = -3

y'(0) = 1

need word file please :

What is a parametrized surface? How does one describe a surface this way, and why is it useful? What are the trade-offs? That is, how does studying parametrized surfaces simplify things, and what complications do we have to deal with? What is regularity in this context, and why is it important?

This question for Discrete Math course. All of them about the same topic!!

Give me a simple definition of each one:

1) Neigbhor of a vertex

2) A connected graph

3) Length of cycle

4) Euler walk

5) Planar graph

6) Chromatic member of graph

7) X(G)

Cost of Common Equity

The future earnings, dividends, and common stock price of Carpetto Technologies Inc. are expected to grow 4% per year. Carpetto's common stock currently sells for $25.50 per share; its last dividend was $2.00; and it will pay a $2.08 dividend at the end of the current year.

1. 
   
2. Using the DCF approach, what is its cost of common equity? Round your answer to two decimal places.
   %
3. 
   
4. If the firm's beta is 1.30, the risk-free rate is 3%, and the average return on the market is 12%, what will be the firm's cost of common equity using the CAPM approach? Round your answer to two decimal places.
   %
5. 
   
6. If the firm's bonds earn a return of 9%, based on the bond-yield-plus-risk-premium approach, what will be r_s? Use the midpoint of the risk premium range discussed in Section 10-5 in your calculations. Round your answer to two decimal places.
   %
7. 
   
8. If you have equal confidence in the inputs used for the three approaches, what is your estimate of Carpetto's cost of common equity? Round your answer to two decimal places.
   %

PROVE THE FOLLOWING RESULT: Using a compass and a straightedge, construct a triangle ABC such that side BC is of length 2, the circumradius is of length 3/2 and the median AA' is of length 2 and is the midpoint of BC.

Last September, I adopted a dog from our local pet shelter, Percy. Percy’s diet at the pet shelter was lacking to say the least and, despite already being skin and bones, he was losing weight. After adopting Percy, it took a little while for him to acclimate to regular dog food and so he continued to lose weight, but at a slower rate. After about a month, Percy finally began to start gaining weight. Over the next two months, the rate at which he was gaining weight was increasing. During our visit to the vet in December, our vet suggested that I may have gone overboard and let him eat too much. She advised that I should reduce the amount I feed Percy and take him on more routine walks. During the month of December, Percy’s weight gain tapered off, and starting in January, he actually began to lose weight. In February the vet was happy with his weight. I followed her recommendation to increase his food slowly, and Percy’s weight loss slowed over the month. During these first couple weeks of March, Percy’s weight actually seems to have stabilized at a healthy weight of 42lbs!

My professor was very excited to see me sign up to present and thought the project was a good idea. When I proposed it, my professor recommended that I should determine the following information to help me graph Percy’s weight as a function

1. Define what corresponds to t=0

2. Find where f'(t) is positive and where it is negative.

3. Find where f'(t) is increasing and where it is decreasing.

Unfortunately, I am having trouble getting started with this. Please explain how to figure out (1), (2) and (3) above. Finally, give a graph of my dog’s weight and explain how you used (2) and (3) to get this graph. I’ll need to define what the axes represent, so be sure to tell me what choices you make for this.

For this question you must give all answers rounded correct to exactly 3 significant figures (instead of decimal places). Recall that leading zeros are not significant (for example 0.0011 has 4 decimal places, but only 2 significant figures). To obtain more decimal places in the numbers Matlab gives you, type "format short g" first.

The article "The Incorporation of Uranium and Silver by Hydrothermally Synthesized Galena'" (Econ. Geology, 1964: 1003-1024) reports on the determination of silver content of galena crystals grown in a closed hydrothermal system over a range of temperature. The temperature X in degrees C and the silver content Y in mol% for 60 determinations are shown below.

x=[391.52 588.45 366.17 540.96 596.58 514.95 475.69 474.88 351.61 436.63 456.86 488.38 374.74 443.82 351.54 565.11 590.69 522.42 381.72 518.06 352.58 536.14 517.94 489.33 421.54 441.43 519.61 481.52 395.17 575.51 499.37 498.19 389.48 458.26 475.10 447.75 494.49 501.62 543.59 371.33 533.00 469.43 408.83 381.22 404.12 351.36 539.92 355.98 428.00 365.14 568.20 577.03 551.79 421.29 486.85 380.51 572.39 526.76 444.83 510.46]

y=[0.24746 0.55195 0.12887 0.55539 0.66253 0.51603 0.26968 0.39588 0.17175 0.18485 0.47286 0.13409 0.45080 0.14408 0.17320 0.45023 0.59793 0.61566 0.47474 0.29009 0.17034 0.53198 0.60392 0.39073 0.06488 0.36118 0.45917 0.23497 0.32195 0.50951 0.51063 0.51979 0.53781 0.36905 0.53801 0.38265 0.27017 0.28500 0.52003 0.11500 0.38495 0.27878 0.44189 0.04065 0.18611 0.26634 0.44847 0.21019 0.19065 0.01236 0.62531 0.49826 0.29920 0.23947 0.31029 0.29353 0.38524 0.63588 0.25503 0.44352]

(a) Fit the linear regression of Y on X using Matlab. What is the estimated intercept term β^0?

(b) What is the estimated slope of the fitted line, β^1?

(c) What is the estimated residual variance s2e?

(d) What is the standard error for β^1?

(e) Give a 95% confidence interval for β^1.

Enter your confidence interval in the form (lower bound, upper bound).

(   ,    )

(f) What is the predicted silver content of galena crystals grown at 500 degrees C?

(g) Construct a 95% prediction interval for silver content when crystals are grown at 500 degrees C.

Enter your prediction interval in the form (lower bound, upper bound).

(   ,    )

Problem 4-11 (Algorithmic)

Edwards Manufacturing Company purchases two component parts from three different suppliers. The suppliers have limited capacity, and no one supplier can meet all the company’s needs. In addition, the suppliers charge different prices for the components. Component price data (in price per unit) are as follows:

Each supplier has a limited capacity in terms of the total number of components it can supply. However, as long as Edwards provides sufficient advance orders, each supplier can devote its capacity to component 1, component 2, or any combination of the two components, if the total number of units ordered is within its capacity. Supplier capacities are as follows:

If the Edwards production plan for the next period includes 1025 units of component 1 and 825 units of component 2, what purchases do you recommend? That is, how many units of each component should be ordered from each supplier? Round your answers to the nearest whole number. If your answer is zero, enter "0".

What is the total purchase cost for the components? Round your answer to the nearest dollar.

$  

What is the effect of the filter on the Fast Fourier Transform of voice signal?

Is quantization visible? How can you tell?