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(12t-12,cos(3mt)-12mt,3t) is Find the value of t for which the tangent line to the curve r(t)= perpendicular to the plane 3x-3+30z=-5. (Type your answer is an integer, digits only, no letters, no plus or minus. Hint. The tangent vector to the curve should be proportional to the normal vector to the plane.) A m/c has a first cost of Rs 3,00,000 & salvage value of Rs 60,000 and a life of 5 years. It is being depreciated according to straight line method. The management is trying to find a replacement at the end of 3 years of its useful life. What market value the management should fetch so that the capital invested in the m/c is fully recovered. for each policy listed, identify whether it is a command-and-control policy (regulation), tradable permit system, corrective subsidy, or corrective tax. In 2019, Joanne invested $90,000 in cash to start a restaurant. She works in the restaurant 60 hours a week. The restaurant reported losses of $68,000 in 2019 and $36,000 in 2020. How much of these losses can Joanne deduct? O $68,000 in 2019; $36,000 in 2020 O $68,000 in 2019; $22,000 in 2020 O $0 in 2019; $0 in 2020 O $68,000 in 2019; $0 in 2020 determine whether the series is convergent or divergent. [infinity] n7 n16 1 n = 1 2: Find the following limits without using a graphing calculator or making tables. Show your work. a) lim x-4 x+x-20/x+4b) lim x-1 x-x-2x / x2+x Question 2 (10 marks) Kelly is employed by Jasper Ltd in Sydney. In July 20XX she transferred to Perth to take up a position with Langfield Ltd an Australian Manufacturing firm. During the year ended 30th June 20XX the following events took place: Received a salary from Langfield Ltd $80,000. Made a capital gain of $3,000 from the sale of 200 shares in Optus Ltd, a public listed company on the Australian Stock Exchange. The shares were acquired in January 2007. Made a capital loss of $1,000 on an antique coin collection. The collection was acquired in March 2006 at a cost of $700. .Kelly indicated that her taxation return for the year ended 30 June of the previous year shows a net capital loss of $2,000 from the sale of shares. Received a uniform allowance of $1,800. Received a $2,000 bonus from her employer on 3rd July 20XX for her excellent performance. Spent $300 towards protective shields (she kept all necessary records). Required Calculate Kelly's taxable income and tax liability for the year ending 30.06.20XX. In your response ensure you state the appropriate legislation, tax rulings or common law cases to support your answer. Given the function f(xx,z)=xln (1-z)+[sin(x-1)]1/2y. Find the following and simplify your answers. a. fx b. fxz consider the following. f(x, y) = x/y, p(5, 1), u = 3 5 i 4 5 j In Class Practice (CH 02) Consider the following accounts and identify each as an asset (A), liability (L), or equity (E). 1. Rent Expense E 6. Accounts Payable 2. Brock, Capital E 7. Unearned Revenue 3. Furniture A 8. Notes Receivable 4. Service Revenue E 9. Brock, Withdrawals A 5. Prepaid Insurance 10. Insurance Expense Consider integration of f(x) = 1 + e^-x cos(4x) over the fixed interval [a,b] = [0,1]. Apply the various quadrature formulas: the composite trapezoidal rule, the composite Simpson rule, and Boole's rule. Use five function evaluations at equally spaced nodes. The uniform step size is h = 1/4 . (The true value of the integral is 1:007459631397...) There are only red marbles and green marbles in a bag. There are 5 red marbles and 3 green marbles. Mohammed takes at random a marble from the bag. He does not put the marble back in the bag. Then he takes a second marble from the bag. 1) Draw the probability tree diagram for this scenario. 2) Work out the probability that Mohammed takes marbles of different colors. 3) Work out the probability that Mohammed takes marbles of the same color. For what value(s) of h and k does the linear system have infinitely many solutions? -4 55 + and k Ix2 kx2 4x1 hx1 to which cache block will the memory address 0x000063fa map? write the answer as a decimal (base 10) number. Part Three: Writing Question Instructions: You are required to answer the question in the spaces provided (4 Marks). 15. Compare and contrast 'Content' and 'Process' motivation perspectives/theories. The function h models the height of a rocket in terms of time. The equation of the function h(t) = 40t-2t - 50 gives the height h(t) of the rocket after t seconds, where h(t) is in metres. (1.1) Use the method of completing the square to write the equation of h in the form h(t)= a(t-h)+k. (1.2) Use the form of the equation in (1.1) to answer the following questions. (a) After how many seconds will the rocket reach its maximum height? (b) What is the maximum height red hed by the rocket? Apply the Gram-Schmidt orthonormalization process to transform the given basis for p into an orthonormal basis. Use the vectors in the order in which they are given. B = {(1, -2, 2), (2, 2, 1), (-2, 1 Given f(x, y) = 2y^2+ xy^3 +2e^x, find fy. fy=6xy + 4yfy = 4xy + xy fy=xy + 8x^y fy = 4y + 3xy Externalities, the Environment and Natural Resources Our very existence makes environmental problems inevitable. Environmental problems are not new. First, explain what is different about the attention we now give to these problems relative to an earlier period of time. Next, debate how our behavior, institutions, and evolution contributed to environmental problems. explain why data should always be entered directly into the field book at the time measurements are made, rather than on scrap paper for neat transfer to the field book later.