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omar butler

omar b.

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a) Solve the rational equation $\frac{x^2 + 1}{x - 1} + x = 2 + \frac{2}{x - 1}$ b) Solve the rational inequality $\frac{x}{7} + \frac{x - 7}{x + 6} \ge 1$. Write your answer with interval notation.

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the diamond is famous for its sparkle because the light coming from it glitters as the diamond is moved about. Why does a diamond exhibit such brilliance? Why does it lose much of its brilliance when placed under water?

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Texts: A frequent mistake made by project managers and/or their organizational sponsors is not appropriately valuing the cost and time requirements for personnel necessary to complete project work. If personnel time is not appropriately valued, either the PM or the sponsor can grossly underestimate the budget required for personnel needs throughout the project. Along the same vein, a frequent source of conflict is that one or the other of the sponsor or project manager will greatly undervalue personnel time. Often, consultants will estimate that a full-time employee will only have approximately 1300 to 1600 hours available for billing (billable hours), although the full-time employee must be paid for 2080. Similarly, consultant labor costs need to account for benefit costs, overhead, profit, and downtime. In part because of these differences, project managers can often be surprised by the cost/hour charged by a consultant for labor. Assume that the project has a need for 1500 hours of environmental specialist time. If you hired someone onto your team, you believe you could hire a reasonably qualified applicant by offering approximately $70K base annual salary. First, set up and explain a calculation and associated inputs which you could use to get to an appropriate hourly rate for estimating the cost of this internal environmental specialist’s time. Assume that the project duration is one year, and the required environmental specialist time can be spread evenly throughout the year. That is, assume you don’t need to worry about resource-leveling. Second, if a contractor could provide a qualified ES and would charge you $100/hour for those 1500 hours, would you recommend bringing on someone as an employee within the project team, or would you prefer to seek contractor-provided personnel support for ES tasks? Explain factors you might consider. Feel free to create reasonable situations at your hypothetical organization which might justify one approach or another. As you might have guessed, this isn’t a one-size-fits-all consideration with a definitive answer, and different project managers and/or organizations will arrive at different conclusions with regard to whether to hire or use contractor support.

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7. Find the standard matrix for the linear transformation $T: \mathbb{R}^2 \to \mathbb{R}^3$ defined by $T(x, y) = (3x - 4y, x + 8y, 3y)$, then find the image of the vector $v = (5, -5)$.

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The compound A3B2 decomposes according to the following stoichiometry: A3B2 \rightarrow 3A + B2. This is a non-elementary reaction and the search for your speed equation was done through two distinct stages Stage I - Experimental - The reaction was carried out several times and it was possible to observe the following: a) At the beginning of the reaction, it appears to be of first order in relation to the reagent. b) At the end of the reaction, it appears to be of second order in relation to the reagent. c) The introduction of product B2 in the feed does not affect the reaction speed. d) The introduction of product A into the feed slows down the reaction rate. Stage II - Theoretical - Two speed mechanisms have been proposed with the aim of verifying if any of them could explain the verified experimental observations. Mechanism I Mechanism II A$_3$B$_2$ \rightarrow A$_2$B$_2$ + A (Stage 1) A$_3$B$_2$ \rightarrow AB$_2$ + 2A (Stage 1) A$_2$B$_2$ + A \rightarrow A$_3$B$_2$ (Stage 2) AB$_2$ + 2A \rightarrow A$_3$B$_2$ (Stage 2) A$_2$B$_2$ \rightarrow 2A + B$_2$ (Stage 3) A$_3$B$_2$ + AB$_2$ \rightarrow 4A + 2B$_2$ (Stage 3) a) Determine the speed equation of this reaction as a function of reagent A3B2 for the two mechanisms. b) Check that the experimental observations are valid for some of the mechanisms. Explain your answer.

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QUESTION 9 A shorter focal length will increase the power of which of the following? I. lens II. mirror a. II only b. Neither I nor II c. Both I and II d. I only QUESTION 10 Which of the following scenarios is a reasonable representation of a nearsighted person wearing proper corrective lenses? a. light passes through a convex lens and then another convex lens b. light passes through a concave lens and then a convex lens c. light passes through a concave lens and then another concave lens d. light passes through a convex lens and then a concave lens

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7 marks] (a) Find $dy/dx$ for $x^3y^2 + \sqrt{x+4y} = 7$ (b) Show that the point $(x, y) = (1, 2)$ lies on the curve defined by the equation in part (a), and find the slope of the tangent line at this point.

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Directions: Identify what is being described in the given statements. Choose your answer in the box below and write it on a separate sheet of paper. Semicircle Secant Minor Arc Diameter Radius 1. It is a chord that passes through the center of the circle. 2. It is half of a circle. 3. It is a line that intersects the circle in two points. 4. It is a segment that joins the center and a point on the circle. 5. It is an arc that is less than a semicircle.

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A. Reduce the following ratio in simplest form/lowest term. 1. 10 : 12 = 2. 9 : 15 = 3. 18 : 24 = 4. 21 : 27 = 5. 40 : 50 = 6. 35 : 40 = 7. 4 : 36 = 8. 10 : 45 = 9. 14 : 24 = 10. 45 : 50 =

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7. A mixture contains 24 quarts of water and acid solution of which 60% is acid. How much of this solution should be drained and replaced with water for the solution to be 40% acid? *

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