Let us have a particle which is moving with a constant velocity v in the laboratory frame. Suppose this particle has a rest mass m and it decays into two photons.

We have to find an expression of the energy of the emitted photons as function of the angle between initial particle direction and the photons propagation direction

A light bulb is connected to a 60-V wall socket. The current in the bulb depends on the time t according to the relation I = (1.414 A) sin[(282.6 Hz)t].

(a) What is the frequency of the alternating current? Hz

(b) Determine the resistance of the bulb's filament? Ω

(c) What is the average power delivered to the light bulb? W

V. Economic Trends or forecast

In this section list the economic trends or business cycles that you feel are relevant to investing. Provide information from Livingstone Survey and The Conference Board's LEI and CEI that may be used to forecast the economy’s direction.

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?

Prepare necessary adjusting entries to correct the errors on all issues (ii) to (v) in the financial statements of GHL for the year ended 31 March 2020 in accordance with relevant HKFRSs.  

(ii) At 1 April 2019 there was a deferred tax liability of $6.6 million in the statement of financial position and no adjustments have been made to this figure at 31 March 2020. This deferred tax liability was solely in relation to the differences between the carrying amount ($90 million) and the tax based ($57 million) of plant and equipment. At 31 March 2020 these figures were $96 million and $54 million respectively for the carrying amount and tax base of plant and equipment. The applicable income tax is 20%. GHL accounts for plant and equipment using cost model under HKAS 16 ‘Property, Plant and Equipment’.

The first tax loss carried forward in respect of the year ended 31 March 2020 is $24 million. GHL has reliable budgets for a total taxable profit of $12 million for the next two financial years. Tax losses can be carried forward indefinitely under the tax law. Fanny used the full amount of tax loss to determine the deferred tax amount and has been reflected in the draft financial statements.

(iii) On 31 March 2020 GHL issued $15 million 5% convertible bonds at par. Interests on the bonds are payable annually in arrears with first payment on 31 March 2021. Issue costs payable to professional advisers were $600,000. The bond can, at the choice of the holders, be redeemed at par on 31 March 2023; or converted on 31 March 2023 into ordinary shares in GHL at the rate of three ordinary shares for every $10 bond held.

In the draft financial statements, the proceeds from the bond issue have been recognized as bonds payable. The issue costs have been classified as an administrative expense. Cash received and paid has been recognized. No other entries have been made. The prevailing market interest rate for similar bonds for equivalent risk, but without conversion rights, is 8% per annum.

(iv) On 1 April 2019, GHL entered into a sale and leaseback agreement for its manufacturing plant. The plant was originally acquired by GHL on 31 March 2009 for $8,910,000, at which point the plant had a useful life of 30 years with no residual value. The sale proceeds of plant from the sale and leaseback agreement were $11.25 million, which is higher than the fair value of the plant of $9.0 million. The plant was leased back on a 20-year lease from 1 April 2019 at an annual rental of $1,105,350 to be paid annually in arrears at 31 March 2020. The sale satisfies HKFRS 15 "Revenue from Contracts with Customers", however, she insisted to account for it as a financing arrangement. The first lease rental is paid and charged to the statement of profit or loss. The sales proceed was treated as a financial liability. The incremental borrowing rate is 15% per annum.  

(v) GHL purchased a factory site in Malaysia on 1 April 2019 with intention for industrial use. Land prices in the area had increased significantly in the years immediately prior to 31 March 2020. Nearby sites had been acquired and converted into residential use. It is felt that, should the GHL's site also be converted into residential use, the factory site would have a market value of $27 million. $1.5 million of costs are estimated to be required to demolish the factory and to obtain planning permission for the conversion. GHL was not intending to convert the site at 1 April 2019 and had not sought planning permission at that date. The current replacement cost and carrying amount of the factory site are correctly calculated as $25.1 million and $28 million respectively as at 31 March 2020 before revaluation. Fanny did not reflect the change in fair value of the factory site even the factory site is measured using the revaluation model under HKAS 16.

The market value of the apple tree in year t is V(t) = 200t − 5t²

b) At what year is the apple tree most valuable? What is the value of the tree?

c) Assume that this tree can be harvested only one time. If the real interest is 3%, when should the tree be harvested? (Round years to the closest integer.)

d) If the real interest is 5%, when should the tree be harvested? Compare your results from c) and d) and comment on your findings. Is this the result as you expected?

e) What will be the value of the apple tree at the time of harvest? What is the value of your asset if you invest the proceedings from harvest into bank account that pays 3% annual rate for the rest of period you calculated in part b)?

39. Find the Parker v. Comm. decision from 1997.

a. What is the citation for this case?

b. How many times has this case been cited by the First Circuit Court of Appeals?

c. Are there any cases that are distinguished from Parker?

Problem 1: The energy E of a particle of mass m moving at speed v is given by: E2 = m2 c4 + p2 c2 (1) p=γmv (2) 1 γ = 1−v2/c2 (3) This means that if something is at rest, it’s energy is mc2. We can define a kinetic energy to be the difference between the total energy of an object given by equation (1) and the rest energy mc2. What would be the kinetic energy of a baseball moving at half the speed of light? Give your answer in Joules but also in tons of TNT equivalent. For context, the worst nuclear weapons are measured in megatons. Do you think we could ever accelerate a baseball to half the speed of light?

Problem 2: As we said in lecture, if you heat something up, it becomes more massive! Imagine you took 1 kg of water and heated it up by 50 deg C. By how much would it’s mass increase because of this heating? You might have to look up the heat capacity of water.

An AC generator supplies an rms voltage of 230 V at 60.0 Hz. It is connected in series with a 0.300 H inductor, a 4.30 μF capacitor and a 256 Ω resistor.

What is the impedance of the circuit?

What is the rms current through the resistor?

What is the average power dissipated in the circuit?

What is the peak current through the resistor?

What is the peak voltage across the inductor?

What is the peak voltage across the capacitor?

The generator frequency is now changed so that the circuit is in resonance.

What is that new (resonance) frequency?

[(Food ^ Drinks => Party) v (Drinks ^ Dance => Party)] => (Party => Drinks)

Convert the left-hand side of this formula (in the brackets) into CNF and then into clauses. Show all steps of deriving the clauses.

1. Convert the right-hand side of this formula (not in the brackets) into CNF and then into clauses. Show all steps of deriving the clauses.