a- Write y as the sum of a vector in span {u} and a vector orthogonal.docx

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a. Write y as the sum of a vector in span {u} and a vector orthogonal to u. b. Compute the distance from y to the line through u and the origin. Solution y=(1,2) and u=(4,-3) Let a vector orthogonal to u be w = (x,y) =>u.w = 0 =>4x-3y = 0 => 4x = 3y If y = 4 => x = 3 w = (3,4) Let y = au + bw where a and b are some constants. => (1,2) = a(4,-3) + b(3,4) = (4a+3b, -3a+4b) => 4a + 3b = 1, -3a + 4b = 2 Solving for a, b we get a = -2/25 and b = 11/25 Therefore y = (-2/25)*u + (11/25)*w Line passing through u, origin is: y+3 = (-3/4)(x-4) =>3x+4y = 0 Distance of y from this line is: Distance = (3*1 + 4*2)/5 = 11/5 .

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A. Identify deficiencies in the evidence gathered by the auditor? B. Discuss the steps involved in setting the preliminary judgment about materiality. Class, the concept of materiality is important in the context of auditing. Materiality is a function of the time, the situation, and the people involved. What is material from the point of view of a bank that lends money to the firm? C. What is material from the perspective of shareholders? Solution Answer : According to the prescribed SA\'s: A. Identifying deficiencies in Audit Method : B. Steps nvolved in preliminary Judgement of Materiality in Audit: The concept of materiality in auditing can be explained as follows: Materiality generally explains that; From the point of view of bank lending money to the firm : C. Perspective of Shareolders: .

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Abacus Co. wishes to maintain a growth rate of 12.4 percent a year, a debtâ€“equity ratio of 1.2, and a dividend payout ratio of 28 percent. The ratio of total assets to sales is constant at 0.92. What profit margin must the firm achieve? Solution Equity multiplier = (1+ debt equity ratio) = 1+1.20 = 2.20 ROE = profit margin x turnover x Equity multiplier = profit margin x 1/0.92Â Â x 2.20 Growth rate = ROE x (1- payout ratio) 0.124 = profit margin x 1/0.92Â Â x 2.20 x (1-0.28) Proit margin = 0.124 x 0.92 / (2.2 x 0.72) = 7.20% .

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a. Which elements are chemically similar to each other? Bromine Phosphorus Calcium Boron Nickel Iodine Fluorine b. Which elements are chemically similar to each other? Oxygen Iron Sulfur Aluminum Iodine Carbon c. Which elements are chemically similar to each other? Lithium Oxygen Lead Manganese Potassium Silicon Solution a) Bromine and iodine are chemically similar. Both comes in group 7A and have almost similar properties. Eventhough fluorine also is in group 7A, it is different from the other two because of its small size and high electronagativity. b) Oxygen and sulphur. They belong to group 6A of the periodic table. They both have six valence electrons. c) Lithium and potassium. They belong to group 1 and contains one valence electron. .

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aja pa 12) Which one of the following statements is false? a larval animal changes into an adult that has a radically different body form, the transformation is called metamorphosis B) Most animals are haploid and reproduce using mitosis C) Animal cells lack cell walls. D) A nimals are multicellular, heterotrophic eukaryotes that obtain nutrients by ingestion. Solution Option (C) is incorrect. Animal cells DO lack cell walls, but they have cell membranes. However, option (B) is also incorrect because most animals are diploid and reproduce with meiosis and mitosis. BUT Animal gametes are haploid and reproduce by mitosis (after being produced through meiosis). .

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All of the following income items are inclusive in an employee gross income except Severance pay for the cancellations of employment Vacation allowance Worker compensation payments Moving expense reimbursements All of the following income items are inclusive in an employee gross income except Severance pay for the cancellations of employment Vacation allowance Worker compensation payments Moving expense reimbursements Severance pay for the cancellations of employment Vacation allowance Worker compensation payments Moving expense reimbursements Solution Vacation allowance .

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Air, initially at 220 kPa and 450 K undergoes a polytropic state change to 374 kPa and 495 K. What is the polytropic exponent of this process? and Saturated water vapor is contained in a rigid container. Heat is then added until the the pressure and temperature become 861.818 MPa and 400 ?C, respectively. What was the initial temperature of the steam? ?C Solution PV n =C PV=nRT V= nRT/P P( nRT/P) n =C P 1 (T 1 /P 1 ) n =P 2 (T 2 /P 2 ) n (T 1 P 2 /T 2 P 1 ) n =P 2 /P 1 n= ln(P 2 /P 1 )/ln(T 1 P 2 /T 2 P 1 )= 1.218944 .

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