Explain or use evidence why each is true or false

If C is any smooth, closed curve then Z C e^{x^2} dx = 0

Let F(x, y) = <P(x, y), Q(x, y)> be a vector field on R 2 and let C be a closed curve formed by the unit circle. If ∂P/∂y = ∂Q/∂x , then R C F · dr = 0.

The coordinate transformation x = u² − v² , y = 2uv maps the quarter-disk S = {(u, v) : u² + v² ≤ 1, v ≥ 0, u ≥ 0} onto the half-disk R = {(x, y) : x² + y² ≤ 1, v ≥ 0}.

If x = g(u, v) and y = h(u, v) is a transformation whose Jacobian is a constant 3, then it must map the square [0, 1] × [0, 1] to a region whose area is 1/3.

The equation in φ = π/12 in spherical coordinates describes a cone in R 3 .

1. Determine whether Rolle's Theorem can be applied to f on the closed interval

(Select all that apply.)

If Rolle's Theorem can be applied, find all values of c in the open interval

such that

(Enter your answers as a comma-separated list. If Rolle's Theorem cannot be applied, enter NA.)

2. The height of an object t seconds after it is dropped from a height of 230 meters is

0.1 kg of air (ideal gas) is contained in a closed, rigid tank of volume 0.04 m^3 at 500 K. A paddle wheel stirs the air and transfers energy to the air at a constant rate of 1 kW for 100s. The temperature of the air increases to 600 K.

(a) What is the final pressure of the air (kPa)

(b)Calculate the heat transfer (kJ) for the process (use a constant, average specific heat)

0.1 kg of air (ideal gas) is contained in a closed, rigid tank of volume 0.04 m^3 at 500 K. A paddle wheel stirs the air and transfers energy to the air at a constant rate of 1 kW for 100s. The temperature of the air increases to 600 K.

(a) What is the final pressure of the air (kPa)

(b)Calculate the heat transfer (kJ) for the process (use a constant, average specific heat)

A small diameter tube closed at one end was filled with benzene to within 20 mm from the top of the tube and maintained at 295 K and atm pressure of 100 kPa with a gentle stream of air blowing across the top. After 30 kilo-seconds (30 x 103 s) the liquid level has fallen to 25.8 mm. The vapor pressure of benzene at 295 K is 13.3 kPa. Calculate the diffusivity of benzene in air. Density of benzene = 800 kg/m3. Molecular weight of benzene = 78 kg/kg mol.

A rigid, closed container contains 0.0700 mol of Ne(g) and a sample of the solid, ammonium nitirite, NH4NO2. Assume that the volumes of solids are negligible compared to the volume of the container. The pressure of the Ne is meausre at 33 degrees celsius and is found to be .409atm.

The container is then heated to 333 degrees celsius and all of the ammonium nitrite decomposes according to the reaction. NH4NO2(s) --> N2(g) + 2H2O(g)

The Ne is not involved in the reastion and is still present. The final pressure in the container after complete decompostion of the NH4NO2 is 3.93 atm. Assuming ideal gas behavior, answer the following questions.

a. What is the volume of the container, in liters? ____L

b. What is the partial pressure of H2O in the containers, at 333 C, when the reaction is complete?

pH2O=____atm

A closed, rigid tank fitted with a paddle wheel contains 2.2 kg of air, initially at 200oC, 1 bar. During an interval of 20 minutes, the paddle wheel transfers energy to the air at a rate of 1 kW. During this time interval, the air also receives energy by heat transfer at a rate of 0.5 kW. These are the only energy transfers. Assume the ideal gas model for the air, and no overall changes in kinetic or potential energy. Do not assume specific heats are constant. Determine the change in specific internal energy for the air, in kJ/kg, and the final temperature of the air, in oC. The answer to the change in internal energy is 818.2 kJ/kg. find the final temperature of the air, in ^oC.

You and your family have recently closed on the purchase of your first home and you are excited. You are in need of furniture and appliances for your new home. You have decided to purchase some of the items from eBay and have found a dining room set and living room furniture from a private seller on eBay’s website. You look at the pictures on the website and notify the seller through email that you would like to purchase these items. The seller responds and asks you if you have any more questions about the furniture and agrees to sell you these items. You pay for the furniture with your bank debit card via PayPal’s website electronically. The seller then has the items shipped to you at your new home. When the furniture arrives, you discover that the sofa is severely damaged on the backside and you contact the seller for a refund. The seller refuses to refund your money and states that the items were sold as-is. What recourse, if any, do you have?

In an essay, answer the following questions:

• Describe what criteria must be present to constitute a legal and binding sales contract.
• Briefly summarize the uniform commercial code and if it applies in this scenario.
• Explain if any criminal laws have been violated as it relates to cyber laws.
• Develop and explain your legal strategy to gain a refund of your money.
• What rights do you have with your bank, eBay, and PayPal

Scenario 26-A. Assume the following information for an imaginary, closed economy. GDP = $110,000 Consumption = $70,000 Private Saving = $8,000 National Saving = $12,000

1. Refer to Scenario 26-A. For this economy, what is the tax amount? Show your work.

2. Refer to Scenario 26-A. For this economy, investment is what amount? .

3 Refer to Scenario 26-A. In this economy is the government running a Surplus or Deficit and what is the amount?

4. Refer to Scenario 26-A. For this economy, government purchases are what amount? Show your work.