When a star collapses it significantly shrinks in size and spins up. Consider a star with a mass of M = 3.3×10³¹ kg and an initial radius of R_i = 7.3×10⁶ km. If the initial period of rotation of the star is T_i = 35.1 days, find the new rotational period after it collapses to a final radius of R_f = 7.3×10³ km. Treat the star before and after the collapse as a solid sphere with uniform mass distribution (which is not true, of course, but good enough for an estimation).

The new rotational period of the star, T_f =

Find the ratio between the final and initial rotational kinetic energies of the star.

The factor by which the kinetic energy of the star increases, KE_f/KE_i =

The increase in the rotational kinetic energy of the star comes from gravity. How much work is done by the gravity force while collapsing the star?

The work done by gravity, W =

The difference between a Roth IRA and a traditional IRA is that in a Roth IRA taxes are paid on the income that is contributed but the withdrawals at retirement are tax-free. In a traditional IRA, however, the contributions reduce your taxable income, but the withdrawals at retirement are taxable. Assume you plan to devote $5,000 to retirement savings in each year. You will retire in 30 years and expect to live for an additional 20 years after retirement.

a. Assume the before-tax interest rate is 5%. What will be your after-tax 20-year retirement consumption stream if you choose to save in a traditional IRA? Assume your tax rate is fixed at 30%.

b. What will be your 20-year retirement consumption stream if you choose to save in a Roth IRA?

c. Which provides better expected results if you expect your tax rate to decrease from 30% today to 25% at retirement?

Part 1 AstroTech Semiconductor incurred the following costs in 2018 related to a new product design:

The development costs were incurred after technological and commercial feasibility was established and after the future economic benefits were deemed probable. The project was successfully completed, and the new product was patented before the end of the 2018 fiscal year.

Required:
Calculate the amount of research and development expense AstroTech should report in its 2018 U.S. GAAP income statement related to this project.

Research and development expense is what?

Part 2

Calculate the amount of research and development expense AstroTech should report in its financial statements according to International Financial Reporting Standards (IFRS).
  

What is the research development expense?

The clay layer below is covered with a layer of fill as shown. Assume the fill is placed instantaneously.

1. Estimate the magnitude of primary consolidation settlement for the clay layer due to placement of the fill.
2. Plot the distribution of pore pressure with depth before the fill is placed.
3. Plot the distribution of pore pressure with depth immediately after the fill is placed.
4. Plot the distribution of pore pressure 10 years after the fill is placed.
5. Determine how long it will take to reach 90% of the final primary consolidation settlement.

Compute the cash flow, tax flow, and after tax flow for the following real estate investment property:

-Gross rents are expected to be $36,000 per year

-Expected vacancy allowance is 5% of gross rents

-Property management fees are 8% of rents collected

-Total estimated operating expenses per year $7,200

-Payment of mortgage per year:

Interest 12,000

Principal 3,000

Total 15,000

-Depreciation allowance for the year is $14,350

-The owner's earned income is $100,000 and his marginal tax bracket is 30%

Compute the following:

A) Before tax cash flow

B) Tax flow (taxable income or loss from property annual operation)

C) Income taxes due or tax savings from annual operation of this investment property

D) Annual after tax cash flow from the property

Gross Profit Method: Estimation of Theft Loss You are requested by a client on September 28 to prepare an insurance claim for a theft loss that occurred on that day. You immediately take an inventory and obtain the following data: Inventory, September 1 $38,000 Sales, September 1–September 28 $51,000 Purchases, September 1–September 28 19,000 The inventory on September 28 indicates that an inventory of $15,000 remains after the theft. During the past year, net sales were made at 50% above the cost of goods sold. Required: 1. Compute the inventory lost during the theft. Round the gross profit percentage to 3 decimal places.

1. Goods in transit which are shipped f.o.b. destination should be
A. included in the inventory of the seller.

B. included in the inventory of the buyer.

C. included in the inventory of the shipping company.

D. none of these answers are correct.

2. What is the primary difference between an ordinary annuity and an annuity due?

A. Annuity due only relates to present values.

B. The timing of the periodic payment.

C. Ordinary annuity only relates to present values.

D. The interest rate.

3. Which of the following properly describes a deferral?

A. Cash is paid in the same time period that an expense is incurred.

B. Cash is paid after expense is incurred.

C. Cash is received after revenue is recognized.

D. Cash is received before revenue is recognized.

4. What is the quality of information that is capable of making a difference in a decision?

A. Materiality

B. Timeliness

C. Faithful representation

D. Relevance

Nate the Skate was an avid physics student whose main non-physics interest in life was high-speed skateboarding. In particular, Nate would often don a protective suit of Bounce-Tex, which he invented, and after working up a high speed on his skateboard, would collide with some object. In this way, he got a gut feel for the physical properties of collisions and succeeded in combining his two passions.* On one occasion, the Skate, with a mass of 117 kg, including his armor, hurled himself against a 801-kg stationary statue of Isaac Newton in a perfectly elastic linear collision. As a result, Isaac started moving at 1.89 m/s and Nate bounced backward. What were Nate\'s speeds immediately before and after the collision? (Enter positive numbers.) Ignore friction with the ground.

2. Every day, you order take-out dinner from the nearby Chinese place and your roommate orders take-out from the shwarma place, which is a little farther away. The Chinese take-out is delivered after an exponential waiting time with mean 10 minutes, whereas the shwarma arrives after an (independent) exponential waiting time with a mean of 20 minutes. Whoever gets their food first always takes pity on the other and shares. (a) Let Sn be the amount of time, over the course of n days, that you and your roommate spend waiting hungrily before some food arrives. Find limn→∞ P[Sn ≤ 7n]. (b) Let Tn be the number of times, over the course of n days, that the Chinese food comes first. Find limn→∞ P[Tn ≤ .6n].