Shauna Coleman is single. She is employed as an architectural designer for Streamline Design (SD). Shauna wanted to determine her taxable income for this year. She correctly calculated her AGI. However, she wasn’t sure how to compute the rest of her taxable income. She provided the following information with hopes that you could use it to determine her taxable income.

1. Shauna paid $4,680 for medical expenses for care related to a broken ankle. Also, Shauna’s boyfriend, Blake, drove Shauna (in her car) a total of 115 miles to the doctor’s office so she could receive care for her broken ankle.
2. Shauna paid a total of $3,400 in health insurance premiums during the year (not through an exchange). SD did not reimburse any of this expense. Besides the health insurance premiums and the medical expenses for her broken ankle, Shauna had Lasik eye surgery last year and paid $3,000 for the surgery (she received no insurance reimbursement). She also incurred $450 of other medical expenses for the year.
3. SD withheld $1,800 of state income tax, $7,495 of Social Security tax, and $14,500 of federal income tax from Shauna’s paychecks throughout the year.
4. In 2019, Shauna was due a refund of $250 for overpaying her 2018 state taxes. On her 2018 state tax return that she filed in April of 2019, she applied the overpayment toward her 2019 state tax liability. She estimated that her state tax liability for 2019 will be $2,300.
5. Shauna paid $3,200 of property taxes on her personal residence. She also paid $500 to the developer of her subdivision, because he had to replace the sidewalk in certain areas of the subdivision.
6. Shauna paid a $200 property tax based on the state’s estimate of the value of her car.
7. Shauna has a home mortgage loan in the amount of $220,000 that she secured when she purchased her home. The home is worth about $400,000. Shauna paid interest of $12,300 on the loan this year.
8. Shauna made several charitable contributions throughout the year. She contributed stock in ZYX Corp. to the Red Cross. On the date of the contribution, the fair market value of the donated shares was $1,000 and her basis in the shares was $400. Shauna originally bought the ZYX Corp. stock in 2009. Shauna also contributed $300 cash to State University and religious artifacts she has held for several years to her church. The artifacts were valued at $500 and Shauna’s basis in the items was $300. Shauna had every reason to believe the church would keep them on display indefinitely. Shauna also drove 200 miles doing church-related errands for her minister. Finally, Shauna contributed $1,200 of services to her church last year.
9. Shauna paid $250 in investment advisory fees and another $150 to have her tax return prepared (that is, she paid $150 in 2019 to have her 2018 tax return prepared).
10. Shauna is involved in horse racing as a hobby. During the year, she won $2,500 in prize money and incurred $10,000 in expenses. She has never had a profitable year with her horse-racing activities, so she acknowledges that this is a hobby for federal income tax purposes.
11. Shauna sustained $2,000 in gambling losses over the year (mostly horse-racing bets) and had only $200 in winnings.

b. Assume Shauna’s AGI is $207,000. Determine Shauna’s taxable income.

Consider the potential well defined by

V(x)= {0 -L/2<x<L/2}

{Vo x>L/2 or x<L/2}

1. For E>Vo (unbound state, find the solutions to the time-independent Schroedinger equation for a particle incident from the left and traveling to the right(Use boundary conditions to evaluate coefficients A-F)

2. Find expressions for the transmission and reflection as a function of energy.

3. Find the necessary conditions for perfect transmission. Interpret this condition on physical grounds (note that k=2pi/gamma, which reflects the wave vector ,k, to the wavelength).

7.11 Consider two cases involving parallel flow of dry air at V = 1 m/s, T_∞ = 45°C, and atmospheric pressure over an isothermal plate at T_s = 20°C. In the first case, Re_x,c = 5 × 10⁵, while in the second case the flow is tripped to a turbulent state at x = 0 m. At what x‐location are the thermal boundary layer thicknesses of the two cases equal? What are the local heat fluxes at this location for the two cases?

Answer: x=.142; q”_lam = -129 W/m²;  q”_turb = -175 W/m²

Shows a new process in which 0.0100 kg of methane (an ideal gas) is compressed from a pressure of 0.100 MPa and a temperature of 20.0 °C to a pressure of 10.0 MPa in a polytropic process with n = 1.35. Determine the moving boundary work required.

Determine the work required in Example 4.5 if the final pressure of the methane is 0.500 MPa.

If the work required in Example 4.5 is ?5.00 kJ, determine the final temperature and pressure of the methane.

If the gas used in Example 4.5 were air, determine the work required to compress it polytropically from 14.7 psia, 70.0°F to 150.°F with n = 1.33.

1. The refractive index of a transparent material can be determined by measuring the critical angle when the solid is in air. If θ_c= 40.1° what is the index of refraction of the material?

2. A light ray strikes this material (from air) at an angle of 35.5° with respect to the normal of the surface. Calculate the angle of the reflected ray (in degrees).

3. Calculate the angle of the refracted ray (in degrees).

4. Assume now that the light ray exits the material. It strikes the material-air boundary at an angle of 35.5° with respect to the normal. What is the angle of the refracted ray?

A maximal plane graph is a plane graph G = (V, E) with n ≥ 3 vertices such that if we join any two non-adjacent vertices in G, we obtain a non-plane graph.

a) Draw a maximal plane graphs on six vertices.

b) Show that a maximal plane graph on n points has 3n − 6 edges and 2n − 4 faces.

c) A triangulation of an n-gon is a plane graph whose infinite face boundary is a convex n-gon and all of whose other faces are triangles. How many edges does a triangulation of an n-gon have?

Using the wave functions

for the potential energy step, apply the boundary conditions of ψ and

dψ/dx

to find B' and C' in terms of A', for the potential step when particles are incident from the negative x direction. Evaluate the reflection and transmission coefficients

R=

and

T=

.

( k₀=42 and k₁=12)

Boundary-Value Problems in Other Coordinate Systems

1. Solve ∆u = 0 in a disk x^2 + y^2 ≤ 25, where u(5, θ) = 7 sin 3θ − 6 sin 8θ and u is bounded when   r = 0.
2. Solve ∆u = 0 in an annulus 1 ≤ x^2+y^2 ≤ 4, where u(1, θ) = 75 sin θ, u(2, θ) = 60 cos θ.
3. Find the steady-state temperature distribution in a disk of radius 1 if the upper half of the circumference is kept at 100◦ and the lower half is kept at 0◦ .