Numerade

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in your view has policing progressed into a new era? if so why do you believe this to be the case

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Compute the products in Exercises 1–4 using (a) the definition, as in Example 1, and (b) the row–vector rules for computer Ax, or, the rule for computing a product Ax in which the i th entry of Ax is the sum of the products of corresponding entries from row i of A and from the vector x. If a product is undefined, explain why. 4) 8 3 1, 5 1 2 |111

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Drag the correct label to the appropriate location to identify the functions of a generalized cell. Functions in lipid metabolism Produces cellular membranes Structural support for cell Produces ribosomal RNA Directs cellular activity Produces cellular energy (ATP) Boundary and gateway around the cell Site of protein synthesis Packages proteins

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What is meant by the term “efficient market?” Can investors routinely beat the market if it is perfectly efficient?

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Solve the system of differential equations $\begin{cases} x' = 12x + 16y \ y' = -8x - 12y \end{cases}$ x(0) = 5, y(0) = -4 The lesser of the two eigenvalues is Its corresponding eigenvector is (a, -1). What is a? a = The greater of the two eigenvalues is Its corresponding eigenvector is (2, b). What is b? b = The solution to the system is x(t) = y(t) =

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4. Recall that the angular momentum about the origin of a particle of mass $m$, velocity $v$, and position $\mathbf{r}$ is $\mathbf{J} = \mathbf{r} \times m\mathbf{v}$. Now consider a rigid collection of particles (or a solid body) rotating about an axis through the origin, the angular velocity of the collection is given by $\mathbf{\omega}$. (a) Show that the velocity of the $i^{th}$ particle is $\mathbf{v}_i = \mathbf{\omega} \times \mathbf{r}_i$. (b) Show that the total angular momentum $\mathbf{J}$ is $\mathbf{J} = \sum_i m_i \left[ \mathbf{\omega} r_i^2 - (\mathbf{r}_i \cdot \mathbf{\omega}) \mathbf{r}_i \right]$. To do this, you may want to use the vector identity $\mathbf{a} \times (\mathbf{b} \times \mathbf{c}) = (\mathbf{a} \cdot \mathbf{c})\mathbf{b} - (\mathbf{a} \cdot \mathbf{b})\mathbf{c}$. (c) Show further that the component of $\mathbf{J}$ along the axis of rotation can be written as $I\omega$, where $I$, the moment of inertia of the collection about the axis or rotation, is given by $I = \sum_i m_i \rho_i^2$. Explain in words what $\rho_i$ is. (d) Using the expression for $I$ above, show that the total kinetic energy of the particles (or solid object) is $\frac{1}{2}I\omega^2$.

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Net Sales Cost of Goods Sold P 2,500,000 1,000,000 Gross Profit P 1,500,000 Selling and Administrative Expenses 550,000 Operating Income P 950,000 Income Tax Expense 285,000 Net Income P 665,000

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QUESTION 3 "3. With regard to the data in Problem 2, what would be a reasonable explanation of the financial results? a. The increase in book value of equity results from an increase in the market value of common shares. b. The decrease in the debt-to-equity ratio indicates that lenders are less willing to extend credit to the business than they have been in the past. c. The increase in book value of equity indicates that the firm may have increased profitability which has not been paid as dividends, the firm may have issued new equity shares, or the firm may have paid less in dividends than in the past to improve its solvency position and reinvest net income in the growth opportunities of the firm."

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A professor holds six office hours per week. Demand for office hours varies wildly as reflected in this historical data. The duration of time to answer questions varies independently from the actual demand. Question duration is reflected in this table. Probability 0.5 0.05 0.1 0 0.05 0.05 0.1 0.1 0.05 # Students per 6 hours 0 1 2 3-9 10 11 12 13 14 Entries in the student demand and question duration tables that reflect a range in demand, i.e.,3-9 students per six hours or 4-9 minutes, should be treated as collapsed entries in the table. Thus, a question duration of 4 minutes has a 0.05 probability, a question duration of 5 minutes also has a 0.05 probability, and so on up through 9 minutes and a 0.05 probability. This table contains random numbers for the number of students and the question duration for a 16-week period. Week # Students Question Duration Week # Students Question Duration Week 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 # Students 82 60 94 94 36 50 21 71 94 22 31 58 81 44 21 34 Duration 20 71 60 80 33 11 32 49 14 36 18 74 97 9 4 96 Use the question duration figure as the time required to answer questions for each student that week, so if three students arrive in week seven and the average duration is ten minutes, the total time spent answering questions that week is thirty minutes. a) Based on the information in the Tables above, what is the total duration spent for answering questions during Week #11? b) Based on the information in the Tables above, what is the highest time spent answering questions for all of the weeks? Please show the interim calculations for probability, cumulative probability, and random number intervals for the # students and the duration of the questions.

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3. FORCES ON A DEFLECTOR CART: A wheeled cart with a 90 degree upward deflector experiences a force when a stationary horizontal jet of water 1 inch in diameter and travelling at a speed of 80 ft/s. Develop an analysis to determine the force on the cart when it is (a) stationary, and (b) moving at a speed $V$ in the same direction as the jet. DISCUSSION: The propulsive power expent is force in the direction of travel times cart speed $V$. Make a graph showing propulsive power vs. cart speed; discuss this result.

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chris m.