h Consider a solid T enclosed by the paraboloid z = x^2 +y^2 and the plane z = 4 (the solid above the paraboloid and below the plane). Let M the (closed) surface representing the boundary surface of T. The surface M consists of two surfaces: the paraboloid M1 and the lid M2. Orient M by an outward normal. Let F=(z,2y,-2)

Compute the integral using the Divergence theorem. Carry out the computation of the triple integral using the spherical coordinates.

A6-10. Suppose the Indian central bank (RBI) increases its target overnight interest rate. In doing so it is clearly trying to increase interest rates in the money market (and throughout the economy).

(d) Although not as open to capital flows as Canada, we can think of India is an open economy. What additional effect will the policy have on aggregate expenditure? [4]

(e) How will aggregate demand be affected, whether we treat the economy as closed or open? [2]

1. Prove that every complete lattice has a unique maximal element.

2. (ii) Give an example of an infinite chain complete poset with no unique maximal element.

3. (iii) Prove that any closed interval on R ([a, b]) with the usual order (≤) is a complete lattice (you may assume the properties of R that you assume in Calculus class).

4. (iv) Say that a poset is almost chain complete if every nonempty chain has an l.u.b. Give an example of an almost chain complete poset with no minimal element.

Netscape planned to offer 3.5 mln shares at $14 in an IPO. A day before the offering their underwriters suggested to change the offer to 5 mln shares at $28. Netscape had an IPO on August 8^th, 1995 -- 5 mln shares at $28 were offered (excluding the 15% overallotment). During the first day of trading, the price of the stock rose to a maximum of $73 and closed the day at $54. How much money did Netscape ‘leave on the table’? For simplicity, disregard the overallotment shares and the underwriter’s spread.

The vapor pressure of an organic solvent is 50mmHg at 25 C and 200mmHg at 45 C. The solvent is
the only species in a closed flask at 35 C and is present in both liquid and vapor states. The volume
of gas above the liquid is 150 mL.

a) Estimate the amount of the solvent (mol) contained in the gas phase.

b) What assumptions did you make? How would you answer change if the species dimerized (one molecule results from two molecules of the species combining?

Solve the scissors, paper, rock game. This game is well known in many parts of the world. Two players simultaneously present a hand in one of three positions: an open hand (paper), a closed fist (rock), or two open fingers (scissors). The payoff is 1 unit according to the rule “Paper covers rock, rock breaks scissors, and scissors cut paper.” If both players present the same form, the payoff is 0.

Set up the payoff matrix for the game and then solve it.

As the global pandemic has not slowed with its spread, many business owners and individuals have considered filing bankruptcy. As part of the health and safety measures, courtrooms have been closed to slow or deter the spread of the virus. A small business owner and her business partner have decided to file bankruptcy as the pandemic has slowed business over the past three months laving uncertain of future business.

•Should debtors with older vehicles be allowed to take an additional deduction for operating expenses? Explain.

On May 1, the share price of Company Monash is $60 and its December futures price is $54.7. On July 1 the share price is changed to $64 and its December futures price is changed to $64. An investor entered into futures contracts on May 1 to hedge his/her purchase of the share of Company Monash on July 1. The investor closed out his/her position on July 1. What is the effective price (after taking account of hedging) paid by the investor?

P6. 3 A 140 -seat dining room had a weekly customer count by meal period and day:

Lunch Dinner

Sunday Closed 180

Monday 160 110

Tuesday 170 112

Wednesday 175 108

Thursday 160 120

Friday 180 210

Saturday 50 250

a. For each meal period and for each day of the week calculate the seat turnover

b. Calculate the average number of customers per day and the average seat turnover for the week for each meal period.