A metal sphere with radius ra is supported on an insulating stand at the center of a hollow, metal, spherical shell with radius rb. There is charge +q on the inner sphere and charge −q on the outer spherical shell. Take V to be zero when r is infinite.

Calculate the potential V(r) for r<r a .

Calculate the potential V(r) for ra<r<rb

Calculate the potential V(r) for r>rb

Find the potential of the inner sphere with respect to the outer.

Use the equation Er=−∂V∂r and the result from part (b) to find the electric field at any point between the spheres (ra<r<rb).

Use the equation Er=−∂V∂r and the result from part (c) to find the electric field at a point outside the larger sphere at a distance r from the center, where r>

I will really appreciate it if you could answer all of them all for me. Thank you :)

1.

use a direct proof to SHOW the following:

The square of an even natural number is even.

The sum of an even and odd number is odd.

The sum of two even number is even.

The sum of two odd number is even.

2.

Examine below compound proposition:

[-p ^ ( p v q ) ] -> q.

(1) Complete truth table

(2) Explain if this IS or IS NOT a tautology, and why.

3.

Determine the satisfiability of the following compound proposition:

(p v -q) ^ (q v -r) ^ (r v -p) ^ (p v q v r) ^ (-p v -q v -r ).

4. Select ALL that is true about the following logical operation between 'p' and 'q.'

p ∧ q.

if, and only if, both p and q are T, the end result will be T (T/F)

only if both p and q are 1 will result in a 1 (T/F)

If only 1 of the variables is 1, the result CAN still be a 1 (T/F)

in 3 of the 4 outcomes, the outcome will be F. (T/F)

Here are four problems (5 pts each) involving the calculation of DG°' for metabolic reactions we have discussed, based on experimentally determined redox potentials. Calculate the DG°' for each reaction using the equation DG°' = -nFDE₀' and the values for E₀' given in Table 1. Show your work and circle your answer.

Table 1. Reduction potentials for reduction half reactions:

1/2 O₂ + 2H⁺ + 2e^- ® H₂O                                              E₀' = +0.82 V

fumarate + 2H⁺ + 2e^- ® succinate                                  E₀' = +0.03 V

oxaloacetate + 2H⁺ + 2e^- ® malate                                 E₀' = -0.17 V

pyruvate + 2H⁺ + 2e^- ® lactate                                       E₀' = -0.19 V

a-ketoglutarate + CO₂ + 2H⁺ + 2e^- ® isocitrate               E₀' = -0.38 V

FAD + 2H⁺ + 2e^- ® FADH₂                                             E₀' = -0.22 V

NAD⁺ + 2H⁺ + 2e^- ® NADH + H⁺                                    E₀' = -0.32 V

CoQ + 2H⁺ + 2e^- ® CoQH₂                                            E₀' = +0.06 V

Problem 1. isocitrate + NAD⁺ ® a-ketoglutarate + CO₂ + NADH

Problem 2. succinate + FAD ® fumarate + FADH₂

Here are four problems (5 pts each) involving the calculation of DG°' for metabolic reactions we have discussed, based on experimentally determined redox potentials. Calculate the DG°' for each reaction using the equation DG°' = -nFDE₀' and the values for E₀' given in Table 1. Show your work and circle your answer.

Table 1. Reduction potentials for reduction half reactions:

1/2 O₂ + 2H⁺ + 2e^- ® H₂O                                              E₀' = +0.82 V

fumarate + 2H⁺ + 2e^- ® succinate                                  E₀' = +0.03 V

oxaloacetate + 2H⁺ + 2e^- ® malate                                 E₀' = -0.17 V

pyruvate + 2H⁺ + 2e^- ® lactate                                       E₀' = -0.19 V

a-ketoglutarate + CO₂ + 2H⁺ + 2e^- ® isocitrate               E₀' = -0.38 V

FAD + 2H⁺ + 2e^- ® FADH₂                                             E₀' = -0.22 V

NAD⁺ + 2H⁺ + 2e^- ® NADH + H⁺                                    E₀' = -0.32 V

CoQ + 2H⁺ + 2e^- ® CoQH₂                                            E₀' = +0.06 V

Problem 3. malate + NAD⁺ ® oxaloacetate + NADH + H⁺

Problem 4. FADH₂ + CoQ ® FAD + CoQH₂

a. The plane x = 2 is

b. Which of the following vectors is not perpendicular to vector u =(-5, 2, 1)?

c.Given unit vectors i, j and k, 2j × 3k=

d. If Car A is travelling north at 50 km/h and Car B is travelling south at 60 km/h, the velocity of Car A relative to Car B is

e. Given three vectors, u, v, and w, if u • (v × w) = 0, what geometrical result can be concluded?

f. The plane (x, y, z) = (4, 2, 1) + s(1, 1, -2) + t(2, -1, 3), converted into scalar form, has equation

An aircraft is in level flight at airspeed v(t) m/s with thrust T(t) N at cruising altitude. Suppose that at v0 = 250 m/s, the aerodynamic drag experienced by the aircraft at this altitude is:

Fd(v) = 0.25v 2 . (1)

Then, an extremely simplified model relating v(t) to T(t) is:

mv˙(t) + Fd(v(t)) = T(t), (2)

where m = 25000 kg. Assume v(t) is always positive.

Question 1. Linearize (2) at v0 = 250 m/s, and an appropriate nominal thrust T0. That is, create a new linear system model ˙δv + aδv = bδT that is accurate for small perturbations δv(t) = v(t) − v0, δT = T(t) − T0.

Question 2. Suppose we want the aircraft to fly at v0 = 250 m/s. However, precise modelling of drag is very difficult. Suppose in reality the dynamics are slightly different:

mv˙(t) + 0.23v(t) 2 = T(t). (3)

To control v(t) to be close to the reference 250m/s, you try using a proportional controller to control the thrust:

T(t) = T0 + k(v0 − v(t)), (4) with k = 100.

Here T0 is the value calculated in Question 1, but the controller is applied to the true dynamics (3). Find the final final value of v in: (a) open loop (i.e. just apply T(t) = T0), and (b) closed loop (using (4)). You may need to solve a quadratic equation. Recall that v(t) is assumed to be positive. Which one is better?

CONVERT CODE FROM JAVA TO C# PLEASE AND SHOW OUTPUT

import java.util.*;

public class TestPaperFolds
{
   public static void main(String[] args)
   {
       for(int i = 1; i <= 4; i++)               //loop for i = 1 to 4 folds
       {
           String fold_string = paperFold(i);   //call paperFold to get the String for i folds
           System.out.println("For " + i + " folds we get: " + fold_string);
       }
   }

   public static String paperFold(int numOfFolds)   //recursive function that returns the FoldSequence string
   {
       if(numOfFolds == 1){       //if numOfFolds = 1, the return "v"
           return "v";
       }
       else{                       //Otherwise make a recursive call to the paperFold(numOfFolds - 1)
           String s = paperFold(numOfFolds -1);
           return flipString(reverseString(s)) + "v" + s;    //reverse the string s, then flip it, then append "v" and s
       }

   }

   public static String reverseString(String s)   //this helper function reverses a string
   {
       String out = "";
       for(int i = s.length()-1; i >= 0; i--)
           out = out + s.charAt(i);
       return out;
   }

   public static String flipString(String s)   //this helper function flips a string
   {
       String out = "";
       for(int i = 0; i < s.length(); i++){
           if(s.charAt(i) == 'v'){               //converts v into ^
               out = out + '^';
           }
           else if(s.charAt(i) == '^'){       //converts ^ into v
               out = out + 'v';
           }
       }
       return out;
   }
}

-----------
Sample Output:
For 1 folds we get: v
For 2 folds we get: ^vv
For 3 folds we get: ^^vv^vv
For 4 folds we get: ^^v^^vvv^^vv^vv

Depreciation for Partial Periods

Clifford Delivery Company purchased a new delivery truck for $54,600 on April 1, 2016. The truck is expected to have a service life of 10 years or 109,200 miles and a residual value of $4,800. The truck was driven 11,300 miles in 2016 and 12,700 miles in 2017. Clifford computes depreciation to the nearest whole month.

Required:

Compute depreciation expense for 2016 and 2017 using the
For interim computations, carry amounts out to two decimal places. Round your final answers to the nearest dollar.
Straight-line method

Sum-of-the-years'-digits method

Double-declining-balance method

Activity method

For each method, what is the book value of the machine at the end of 2016? At the end of 2017?
(Round your answers to the nearest dollar.)
Straight-line method

Sum-of-the-years'-digits method

Double-declining-balance method

Activity method

The book value of the asset in the early years of the asset's service will be under an accelerated method as compared to the straight-line method. The method is appropriate when the service life of the asset is affected primarily by the amount the asset is used.

Bean Delivery Company purchased a new delivery truck for $58,200 on April 1, 2016. The truck is expected to have a service life of 5 years or 122,400 miles and a residual value of $4,800. The truck was driven 9,000 miles in 2016 and 10,700 miles in 2017. Bean computes depreciation to the nearest whole month.

Required:

Compute depreciation expense for 2016 and 2017 using the
For interim computations, carry amounts out to two decimal places. Round your final answer to the nearest dollar.
Straight-line method

Sum-of-the-years'-digits method

Double-declining-balance method

Activity method

For each method, what is the book value of the machine at the end of 2016? At the end of 2017?
(Round your answers to the nearest dollar.)
Straight-line method

Sum-of-the-years'-digits method

Double-declining-balance method

Activity method

The book value of the asset in the early years of the asset's service will be under an accelerated method as compared to the straight-line method. The method is appropriate when the service life of the asset is affected primarily by the amount the asset is used.

Dr. Trudeau’s little experiment had a big impact on medical thinking at the time. His experiment offered a rationale for opening his Adirondack Cottage Sanitarium, which offered rich and poor alike a regimen of abundant nourishing food, lots of sunlight, plenty of rest, and as much fresh air as a person could tolerate. Hundreds were helped, and many similar establishments were opened. Perhaps the experiment was so successful because of the care with which Trudeau had designed its components. It is important to identify an interesting and potentially approachable question or set of questions before undertaking an experiment. But it is just as important to devise a clever experimental design. When we design an experiment, we choose the treatments that will be received and we control or manipulate them in appropriate ways. These treatments or manipulations are the independent variable(s). The observed or measurable differences in outcome for the treatment groups are the dependent variable(s). Suppose I want to know how much sunlight is needed to produce the sweetest oranges? Based on what I know about sunlight and photosynthesis, I hypothesize that the greater amount of sunlight an orange plant gets, the sweeter the juice of the orange. To investigate whether this is true, I might place one group of plants in the sun for 2 hours per day, another group for 4 hours per day, and nother group for 8 hours per day. At the end of the experiment, I could test for the amount of sugar in the juice of the oranges. The amount of time in the sun is the independent variable. The sugar in the juice is the dependent variable.

7. What is the dependent variable in the Rabbit Island Experiment? Also, list all of the independent variables you can think of in the experiment. (Hmm, maybe Dr. Trudeau’s experiment was not so simple after all!)

8. Often, scientists like to hold all conditions constant except one. Just varying one thing at a time makes it easier to analyze the results. Select any one of the independent variables you have listed above and design an experiment similar to Dr. Trudeau’s. State your experimental question, i.e., what are you trying to find out. Formulate a hypothesis. Then decide upon and write out a description of how you will manipulate your treatment groups (there needn’t be three; you could have two, or four—just design a good experiment!), and then imagine the possible outcomes, assuming survival is the dependent variable. Now generate two survival curves based on those imagined outcomes—one that supports your hypothesis and one that does not. Give possible percent survival rates for each experimental group under both outcomes.