Numerade

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Step 2 Next, find $ f_{y}(x, y) $. \[ \begin{array}{l} f_{y}(x, y)=\frac{\partial}{\partial y}\left(\frac{x}{x^{2}+y^{2}}\right) \\ =\frac{\left(\left(x^{2}+y^{2}\right) \cdot 0-20-2 x y\right)}{\left(x^{2}+y^{2}\right)^{2}} \\ =\frac{-2 \cdot x y}{\left(x^{2}+y^{2}\right)^{2}} \\ \end{array} \] Step 3 Therefore, \[ \begin{aligned} \nabla f(x, y) & =f_{x}(x, y) \hat{i}+f_{y}(x, y) j \\ & =\frac{y^{2}-x^{2}}{\left(x^{2}+y^{2}\right)^{2}} \mathbf{i}+\frac{-2 x y}{\left(x^{2}+y^{2}\right)^{2}} \mathbf{j} . \end{aligned} \] The level curve for $ c=\frac{1}{4} $ is given by $ f(x, y)= $

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Question 4 (1 point) What is the power required to accelerate a 10 kg mass from a velocity of 5 m/s to a velocity of 15 m/s in 3 seconds? 333 W 225 W 167 W 33 W

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Which of the following is NOT an example of a factor of production? A. entrepreneurship B. capital C. competition D. natural resources E. labor

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6. When two clerks share the same cash register it is a violation of which internal control principle? a. Establish responsibilities. b. Maintain adequate records. c. Insure assets. d. Bond key employees. e. Apply technological controls. 7. An income statement account that is used to record cash overages and cash shortages arising from omitted petty cash receipts and from errors in making change in titled the a. Cash Lost account. b. Bank Reconciliation account. c. Petty Cash account. d. Cash Over and Short account. e. Cash Receivable account. 8. Costs included in the Merchandise Inventory account can include all of the following EXCEPT: a. damaged inventory that cannot be sold. b. storage. c. invoice price minus any discount. d. insurance. e. transportation-in. 9. An analysis that explains differences between the checking account balance according to the depositor's records and the balance reported on the bank statement is a(n): a. bank audit. b. internal audit. c. analysis of debits and credits. d. bank reconciliation. e. trial reconciliation. 10. Outstanding checks refer to checks that have been: a. held as blank checks. b. written, recorded, sent to payees, and received and paid by the bank. c. issued by the bank. d. written and not yet recorded in the company books. e. written, recorded on the company books, sent to the payee, but not yet paid by the bank.

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For the circuit in Fig. 1.3, use the Thevenin equivalent across terminals ab to find the voltage $V_o$ across the 8 $\Omega$ resistor. Note, you need to find the Thevenin equivalent to the left of the 8 $\Omega$ resistor and then use it to find the voltage across the 8 $\Omega$ resistor.

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Cheyenne Inc. has issued three types of debt on January 1, 2017, the start of the company's fiscal year. (a) $11 million, 10-year, 14% unsecured bonds, interest payable quarterly. Bonds were priced to yield 10%. (b) $28 million par of 10-year, zero-coupon bonds at a price to yield 10% per year. (c) $20 million, 10-year, 8% mortgage bonds, interest payable annually to yield 10%. Prepare a schedule that identifies the following items for each bond: (1) maturity value, (2) number of interest periods over life of bond, (3) stated rate per each interest period, (4) effective- interest rate per each interest period, (5) payment amount per period, and (6) present value of bonds at date of issue. (Round stated and effective rate per period to 2 decimal places, e.g. 10.25%. Round present value factor calculations to 5 decimal places, e.g. 1.25124 and the final answer to 0 decimal places e.g. 58,971.) Unsecured Bonds Zero-Coupon Bonds (1) Maturity value $ $ $ (2) Number of interest periods (3) Stated rate per period % % (4) Effective rate per period % % (5) Payment amount per period $ $ $ (6) Present value $ $ $ Mortgage Bonds % %

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1. Conducting spheres are located at $r_1 = 10$ [mm] and $r_2 = 20$ [mm] as shown below. The region between the conducting spheres are filled with dielectric with material parameter, $2\epsilon_0$. Inner sphere conductor ($r_1 = 10$ [mm]) is connected to 100 [V] source and outer sphere conductor ($r_2 = 20$ [mm]) is connected to 0 [V] (GND). (a) Find the location of 20 [V] equipotential surface and draw the distribution. Show ALL DETAILED STEPS for your analysis. (Hint) Start from Laplace Equation to find voltage distribution (b) Find the capacitance for the conductor. Show ALL DETAILED INTERMEDIATE STEPS for your analysis. (Hint) Find voltage, V, from Laplace Equation. Use boundary conditions to find total charge, Q.

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Following mathematical equations, write the Excel formulas and solve them using Excel software. Set up a spreadsheet by placing the value of each variable in the cell stated and label each variable in the cell to the left (Column A). Put a heading as shown on each column and place a border around each cell. Below the above-stated spreadsheet, calculate to two decimal places and label each Y value (Y1 through Y6). Show the respective Excel formula in text form to the right of each Y value on the worksheet. (8 points: a-d 1 pt., d and c 2 pts each) Variable Value Cell Location Example g 2 B7 a 4.0 B8 b -3.1 B9 c 4.6 B10 X 5.0 B11 Z 2.5 B12 Degrees 30 B13 (Degrees) 20 B14 Note: Pi and c is exponential Example Y0 = sin(g) (see formula example in template) Y1 = 3x - 1.5 Y2 = 2x * x + 3z + 5 Y3 = 2x + c + e Y4 = x^5 + b + c^3 - 4xc + In + 2a^2 Y6 = e(x/2cos)

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T-Mobile LTE 3 of 3 4:59 PM 66% action u (x1, x2) = x1^1/3x2^2/3, Derive her demand functions for goods 1 work. (20 points) Question 4 A. For the utility function u(q1, q2) = 3q1 + 2q2, write down the equation of an indifference curve with utility level 80, draw a diagram, calculate the intercepts, and calculate the slope of the indifference curve. What is the MRS (the rate which consumer is willing to substitute good 2 for good 1 and stay at the same utility level)? (10 points) B. For the utility function in part A, derive the demand functions for the two goods, when price of good 1 is $4 and price of good 2 is $3. Assume income is Y. (10 points) Question 5 Suppose Lin's preferences have the following properties: completeness, transitivity, more is better, extremes better than averages. Draw her indifference map, show the direction of increase in utility. (5 points)

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The image below shows an example of a Boolean expression simplified (minimized). Provide only the explicit names of Boolean algebra laws used at each step of this transformation process. Simplification Example: (AB + ABA + B = ABABA + B = A + BA + BA + B = A + BAA + AB + BA + BB = A + BA + AB + AB + BB = A + BA1 + B + B + BB = A + BA1 + BB = A + BA = AA + AB = AB)

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nicholas c.