We spent an entire semester talking about Newtonian mechanics (F=ma, KE=1/2 mv2) so that knowledge must be important. The truth is that those equations are almost precisely correct except for the fastest particles. Let's see if we can find out how fast something must be going for those approximations to be off by a signficant amount. Assume we have a object with a mass of mo = 1gram.

1) What is the object's Newtonian kinetic energy at this velocity?K= J

2)Look to see how much the two values of kinetic energy differ. Now the object is going 0.12 c. What is the object's velocity?v = m/s

3)What is the object's relativistic kinetic energy at this velocity?K= J

4)What is the object's Newtonian kinetic energy at this velocity?K= J

5)Now we're going really fast. Look to see how much the two values differ now. Next, the object is going 0.59 c. What is the object's velocity?v = m/s

6)What is the object's relativistic kinetic energy at this velocity?K= J

7)What is the object's Newtonian kinetic energy at this velocity?K= J

8)Next, the object is going 0.95 c. What is the object's velocity?v = m/s

9)What is the object's relativistic kinetic energy at this velocity? K= J

10)What is the object's Newtonian kinetic energy at this velocity?K= J

2. Assume that X1, . . . , Xn are independent copies of the random variable X = Y + V , where Y ∼ N(µ, σ² ) and V ∼ U(−ν, ν), ν > 0, and Y and V are independent. We will consider the hypotheses

H₀ : µ = µ₀ and

H_A : µ does not equal µ₀.

(a) It can be shown that E(X) = µ and var(X) = σ² + ν²/3. Set µ = 60, σ = 3, and ν = 4. Estimate E(X) and var(X) using Monte Carlo simulations based on drawing n = 10⁵ i.i.d. copies of X. You can only use the runif function to generate draws from a distribution, so you will need to take the necessary steps to draw realizations from the appropriate distributions. Comment on the results.

(b) Let T = (√ n) * (Xbar − µ₀)/S be the usual t-test test statistic. Perform a simulation to check whether the distribution of T is well approximated by a t-distribution with n−1 degrees of freedom when n = 20, µ = µ₀ = 65, σ = 3, and ν = 4. Use a QQ-plot (you may use the qt function) and set reps = 1e4. Comment on the results.

(c) Set n = 20, µ₀ = 68, µ = 66, ν = 5, and α = 0.05. Produce a plot of a simulated estimate of the power curve of this test formed by increasing σ from 0.5. Select the sequence of values for σ so that the simulated estimate of the power decreases from roughly 80% to roughly 20%. Comment on the results.

From Jon Kleinberg's "Networks, Crowds, and Markets":

19.8 #5.) Continuing with the diffusion model from Chapter 19, recall that the threshold q was derived from a coordination game that each node plays with each of its neighbors.

Specifically, if nodes v and w are each trying to decide whether to choose behaviors A and B, then:

• if v and w both adopt behavior A , they each get a payoff of a > 0;

• if they both adopt B, they each get a payoff of b > 0; and

• if they adopt opposite behaviors, they each get a payoff of 0.

The total payoff for any one node is determined by adding up the payoffs it gets from the coordination game with each neighbor. Let’s now consider a slightly more general version of the model, in which the payoff for choosing opposite behaviors is not 0, but some small positive number x. Specifically, suppose we replace the third point above with:

• if they adopt opposite behaviors, they each get a payoff of x , where x is a positive number that is less than both a and b.

Here’s the question: in this variant of the model with these more general payoffs, is each node’s decision still based on a threshold rule? Specifically, is it possible to write down a formula for a threshold q , in terms of the three quantities a , b , and x , so that each node v will adopt behavior A if at least a q fraction of its neighbors are adopting A , and it will adopt B otherwise?

In your answer, either provide a formula for a threshold q in terms of a, b, and x; or else explain why in this more general model, a node's decision can't be expressed as a threshold in this way.

Ch 26

32. A power pack charging a cell phone battery has an output of 0.4 A at 5.2 V, both rms. If the power pack is plugged into a 120 V wall socket, what is the rms current? 17.3 mA

33. A neon sign transformer has a 450 Watt AC output with an rms voltage of 15kV when connected to a normal household outlet. There are 500 turns of wire in the primary cell.

a) How many turns of wire are in the secondary coil? 62,500 turns

b) When the transformer is running full power. What is the current in the secondary coil? 30 mA

c) When the transformer is running full power. What is the current in the primary coil? 3.75 A

34. A generator produces 250 kW of electric power at 7.2 kV. The current is transmitted to a remote location through wires with a total resistance of 15 W.

a) What is the power loss due to the resistance in the wires? 18 kW

b) What is the power loss if the voltage increased to 30 kV? 1 kW

35. A 20 µF capacitor is connected across an AC generator that produces a peak voltage 6 Volts. The peak current is 0.2 A. What is the oscillation frequency in Hz? 265 Hz

36. A 500 µH inductor is connected across an AC generator that produces a 3.5 V rms Voltage. What is the frequency if the peak current is 50 mA? 31.5 kHz

37. An FM radio station broadcasts at a frequency of 103.5 MHz. What inductance should be paired with a 10 pF capacitor to build a receiver circuit for this station? 236 nH

A 400 V,50 Hz, six-pole three-phase induction motor drives a constant load of 140 N.m. The motor has the following parameters
?1=0.294 Ω
?1=1.39 ??
??=41 ??
?2′=0.156 Ω
?2′=0.74 ??

1) Starting.
Calculate the following:
i) Motor starting current.
ii) Motor starting torque.

2) Maximum operating point. Calculate the following:
i) Slip at which maximum torque is developed.
ii) Maximum torque developed.

3) Steady-state operation.
Calculate the following:
i) Motor slip.
ii) Motor speed.
iii) Motor current.
iv) Motor power factor.
v) Motor input power.
vi) Motor output power.
vii) Motor efficiency.

4) Speed control of the induction motor:
We need to control the speed of the load by controlling the speed of the induction motor using the ?/? method. The load should be driven at 700 rpm at the same slip obtained in part   3-i above. Calculate the following:
i) The source line-line voltage and frequency.
ii) Motor current.
iii) Motor power factor.
iv) Motor input power.
v) Motor output power.
vi) Motor efficiency.

vii) The line voltage control method can not be used here to reduce the motor speed to 700 rpm, Why? Fully explain your answer.

Notes:
- For calculation:
▪ Use the recommended IEEE equivalent circuit.
▪ Use five decimal digits.
▪ Make sure all equations and numbers are clear.

What is missing?

Assessment Question Week 2: Production Possibility Frontier
In 2017, Nepal production of rice and machinery in 2017 was published by the Nepal Bureau of Statistics as indicated by the table below.
Production in Nepal
   P   Q   R   S   T   U   V   W   X   Y   Z
Rice (1000 tons)   0   10   26   37   45   50   55   59   66   77   80
Machinery (units)   90   89   85   80   75   70   65   60   50   30   0

Based on the table above, a production possibility frontier for Nepal can be plotted as below:

Use the Nepal production table and production possibility frontier to answer the following questions.
(a)   Name positions B, V and D. Explain the implications of each of the production positions (B, V, D) on Nepal’s economy.
(b)   Supposing Nepal is operating at level T what is the opportunity cost of producing 10,000 more tons of rice? Also, suppose Nepal is operating at X what is the opportunity cost of producing 70 units of machinery?
 
(c)   Use the graph below to answer the questions that follow

(i)   Suppose Nepal begins to manufacture fertilizers, explain the impact of the discovery of fertilizers to Nepal’s economy using PPF.
(ii)   Supposing there is a discovery of steel in Nepal, explain the impact of steel to the economy of Nepal using a PPF.
(iii)   The Minister of Finance in Nepal advices that in order to increase rice production and machinery, each sector requires USD 50 billion. Explain the impact of the budgetary allocation on the economy of Nepal using PPF.

java code

Write a program that gives the user a menu of six choices (use integers) to select from. The choices are circle, triangle, cone, cylinder, sphere, and quit. (The formulas are given below.) Once the figure is calculated, an informative message should be printed and the user shown the menu again, so that another choice can be made. The formulas are:

• Area of circle: a = 3.14 * radius * radius
• Area of triangle: a = ½ base * height
• Volume of a cone: v = 1/3 * 3.14 * radius * radius * height
• Volume of a cylinder: v = 3.14 * radius * radius * height
• Volume of a sphere: v = 4/3 * 3.14 * radius * radius * radius

this is what i have so far

public static void main(String[] args) {
  

   }

   public static void menu( String input) {

   if
  
  
   }
  
   public static void circle( double raduis) {
       double area = 3.14*raduis*raduis;
       System.out.println("the area of cirle is :"+ area);
      
      
      
   }
   public static void triangle( double base, double height) {
       double area = 1/2*base*height;
      
       System.out.println("the area of the triangle is :"+ area);
      
      
   }

  
  
   public static void cone( double raduis, double height ) {

       double volume = 1/3*3.14 * raduis *raduis* height;
      
       System.out.println("the volume of the cone is :"+ volume);
      
   }

  
   public static void cylinder(double raduis, double height) {
      
       double volume = 3.14* raduis*raduis* height;
      
       System.out.println("the volume of the cylinder is :"+ volume);
      
      
   }
   public static void sphere(double raduis) {

       double volume = 4/3*3.14 * raduis *raduis*raduis ;
       System.out.println("the volume of the sphere is :"+ volume);
      
   }
  

}

Create individual python code cells for each of the three problems below. In each code cell, use any additional variables and comments as needed to program a solution to the corresponding problem. When done, download the ipynb file and submit it to the appropriate dropbox in the course's canvas page

. 1.

a. Cell Number 1 * Recreate the same list of dictionaries you used during assignment 2.09. (Scroll down to see assignment 2.09 instructions) * Create another variable and define it as an empty list. It will store middle names, so name the variable appropriately. * Loop through the list of dictionaries using a `for` loop, and add each middle name to the list created to hold middle names in the previous bullet point.

b. Cell Number 2 * Create a variable and assign it the length of the middle names list created in the previous cell. Use the appropriate instruction to calculate the length instead of just typing the correct number, which is known as hard-coding. (Hint: You don't have to redefine the list in the new cell as long as you ran the previous cell recently) * Use a `while` loop to count up to the length of the middle names list, and print out the index and value of each item in the list using a format string. (Hint: start your counter at `0` and stop iterating before you reach the length by using a `<` operator)

c. Cell Number 3 * Loop through the list of dictionaries defined in the first cell using another `for` loop. (Hint: Again, you do not need to redefine the list of dictionaries from the previous cell as long as you executed it recently) * Nested inside of that loop, loop through the keys in the current dictionary using another `for` loop and the `enumerate()` instruction. * Nested inside of the nested loop, print out the key and value using a format string. (Hint: You'll need to use the key to get the value out of the dictionary) * Also inside of the nested loop, once the index is greater than or equal to 2, break out of the loop.

2.09 assingment instructions for question 1

**Requirements:** * Create a list containing separate dictionaries for at least 3 people (family members, actors, invisible friends, etc.) and assign the list to a variable. Instead of using your actual family members' names, I want you think of different names starting with the same letter as your family member so that I can't be accused of identity theft. * Each person dictionary should have at least 4 key/value pairs: * first name * middle name. * age (rounded to the nearest decade) * your favorite thing about them * Be sure to use the same keys for each person (eg. "first_name" for everyone's first names). * Print out the entire list.