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allen bennett

allen b.

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3 -5 1 1 1 1 9. -1 5 -2 3 -7 8 -1 6 6 10. 3 -8 3 1 -2 6 1 -4 -3 1 2 5 1 3 5 -1 1 -4 -1 -3 1 11. 12. -1 4 -3 0 2 3 1 -4 7 1 5 2 1 2 1 1 5 8 In Exercises 13 and 14, the columns of $Q$ were obtained by applying the Gram-Schmidt process to the columns of $A$. Find an upper triangular matrix $R$ such that $A = QR$. Check your work. $A = \begin{bmatrix} 5 & 9 \\ 1 & 7 \\ -3 & -5 \\ 1 & 5 \end{bmatrix}$, $Q = \begin{bmatrix} 5/6 & -1/6 \\ 1/6 & 5/6 \\ -3/6 & 1/6 \\ 1/6 & 3/6 \end{bmatrix}$ 13. $A = \begin{bmatrix} -2 & 3 \\ 5 & 7 \\ 2 & -2 \\ 4 & 6 \end{bmatrix}$, $Q = \begin{bmatrix} -2/7 & 5/7 \\ 5/7 & 2/7 \\ 2/7 & -4/7 \\ 4/7 & 2/7 \end{bmatrix}$ 14. 15. Find a QR factorization of the matrix in Exercise 11. 16. Find a QR factorization of the matrix in Exercise 12.

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Gross profit margin is an important ratio of merchandising firms because: Select one: O a. their investments in real property are high Ob. cost of goods sold is usually the largest expense Oc. selling expenses, like advertising, are usually quite high Od. it measures their ability to collect receivables

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Why is analyzing free cash flow (FCF) important for investors? It shows the company’s sales trend. It indicates the cash available for distributing to shareholders. It reveals the company’s total debt. It outlines employee compensation.

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Question Which of these shows the graph of $f(x) = 11^x$? Select the correct answer below:

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2. Professor Alex only eats Grape-nuts<sup>TM</sup> and oat-milk together. He needs 1 gallon of oat-milk (denoted $m$) for every 3 boxes of Grape-nuts<sup>TM</sup> (denoted $g$). (a) Write a utility function for his preferences: $u(g,m) = ...$ (b) The price per box of Grape-nuts<sup>TM</sup> is 5 and the price per gallon of oat-milk is 7. His budget for the week's breakfasts is 77. How much Grape-nuts<sup>TM</sup> and oat-milk should he buy (recall, we allow fractional units)? What is his highest achievable utility?

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1 Two loads are connected in parallel across a 11-kV, 60 Hz supply. Load 1 is rated at 100 kVA, 0.85 power factor lag and load 2 is rated at 120 kW, unity power factor. It is desired to raise the power factor to unity by connecting a lossless capacitor in parallel to the loads. Find the value of this capacitor.

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6. You're a seller of some good and face a linear demand. The current equilibrium price, $p^+$ and the quantity, $q^+$ are $2.00 and 100 units, respectively. Furthermore, you learn that the price elasticity of demand at the equilibrium price is -0.2. Due to changes in market conditions your supply function has changed to $S(p) = -20 + 10p$. What will be the new equilibrium price and quantity?

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P 105 100 95 90 85 80 70 65 60 55 20 15 10 5 MC ATC MR Demand ++++ 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100105110115120 Q

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4. (20 points + 10 point bonus) What data types are allowed in the test expression of a switch and what kinds of values can be used with case expressions in switch statements? For a 10 point bonus, why are floats and doubles not allowed in the test expression of a switch statement?

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1. In the system shown in the figure, k1=k, k2=2k, and k3=3k are given as m1=m and m2=m. Find the eigenvectors and mode shapes when k=10N/m and m=10kg.

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