Inequalties Of Combined Functions2[1]

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Inequalties of Combined Functions Examples and Answers 8.4

Example 1 ,[object Object],[object Object],[object Object],[object Object],8.4

[object Object],[object Object],[object Object],[object Object],[object Object],8.4

[object Object],[object Object],[object Object],8.4

[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],8.4

Example 2 ,[object Object],[object Object],8.4

Solution ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],8.4

[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],8.4

Example 3 ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],8.4

Solution ,[object Object],[object Object],[object Object],[object Object],8.4

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167 c h a p t e r 4 Optimized Implementation of Logic Functions Chapter Objectives In this chapter you will learn about: • Synthesis of logic functions • Analysis of logic circuits • Techniques for deriving minimum-cost implementations of logic functions • Graphical representation of logic functions in the form of Karnaugh maps • Cubical representation of logic functions • Use of CAD tools and VHDL to implement logic functions 168 C H A P T E R 4 • Optimized Implementation of Logic Functions In Chapter 2 we showed that algebraic manipulation can be used to find the lowest-cost implementations of logic functions. The purpose of that chapter was to introduce the basic concepts in the synthesis process. The reader is probably convinced that it is easy to derive a straightforward realization of a logic function in a canonical form, but it is not at all obvious how to choose and apply the theorems and properties of section 2.5 to find a minimum-cost circuit. Indeed, the algebraic manipulation is rather tedious and quite impractical for functions of many variables. If CAD tools are used to design logic circuits, the task of minimizing the cost of implementation does not fall to the designer; the tools perform the necessary optimizations automatically. Even so, it is essential to know something about this process. Most CAD tools have many features and options that are under control of the user. To know when and how to apply these options, the user must have an understanding of what the tools do. In this chapter we will introduce some of the optimization techniques implemented in CAD tools and show how these techniques can be automated. As a first step we will discuss a graphical approach, known as the Karnaugh map, which provides a neat way to manually derive minimum-cost implementations of simple logic functions. Although it is not suitable for implementation in CAD tools, it illustrates a number of key concepts. We will show how both two-level and multilevel circuits can be designed. Then we will describe a cubical representation for logic functions, which is suitable for use in CAD tools. We will also continue our discussion of the VHDL language. 4.1 Karnaugh Map In section 2.6 we saw that the key to finding a minimum-cost expression for a given logic function is to reduce the number of product (or sum) terms needed in the expression, by applying the combining property 14a (or 14b) as judiciously as possible. The Karnaugh map approach provides a systematic way of performing this optimization. To understand how it works, it is useful to review the algebraic approach from Chapter 2. Consider the function f in Figure 4.1. The canonical sum-of-products expression for f consists of minterms m0, m2, m4, m5, and m6, so that f = x1x2x3 + x1x2x3 + x1x2x3 + x1x2x3 + x1x2x3 The combining property 14a allows us to replace two minterms that differ in the value of only one variable with a single product term that does not include that variable a.

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MATH133 UNIT 2: Quadratic Equations Individual Project Assignment: Version 2A Show all of your work details for these calculations. Please review this Web site to see how to type mathematics using the keyboard symbols. Problem 1: Modeling Profit for a Business IMPORTANT: See Question 3 below for special IP instructions. This is mandatory. Remember that the standard form for the quadratic function equation is y = f ( x ) = ax 2 + bx + c and the vertex form is y = f ( x ) = a ( x – h ) 2 + k , where ( h , k ) are the coordinates of the vertex of this quadratic function’s graph. You will use P ( x ) = −0.2 x 2 + bx – c where (−0.2 x 2 + bx ) represents the business’ variable profit and c is the business’s fixed costs. So, P ( x ) is the store’s total annual profit (in $1,000) based on the number of items sold, x . 1. Choose a value between 100 and 200 for b . That value does not have to be a whole number. 2. Think about and list what the fixed costs might represent for your fictitious business (be creative). Start by choosing a fixed cost, c , between $5,000 and $10,000, according to the first letter of your last name from the values listed in the following chart: If your last name begins with the letter Choose a fixed cost between A–E $5,000–$5,700 F–I $5,800–$6,400 J–L $6,500–$7,100 M–O $7,200–$7,800 P–R $7,800–$8,500 S–T $8,600–$9,200 U–Z $9,300–$10,000 4.Replace b and c with your chosen values in Parts 1 and 2 in P ( x ) = −0.2 x 2 + bx − c . This is your quadratic profit model function. State that quadratic profit model functions equation. 5. Next, choose 5 values of x (number of items sold) between 500 and 1,000. Think about the general characteristics of quadratic function graphs (parabolas) to help you with choosing these 5 values of x . 6. Plug these 5 values into your model for P ( x ), and evaluate the annual business profit given those sales volumes. (Be sure to show all of your work for these calculations.) 7. Use the 5 ordered pairs of numbers from 5 and 6 and Excel or another graphing utility to graph your quadratic profit model, and insert the graph into your Word answer document. The graph of the quadratic function is called a parabola . 8. What is the vertex of the quadratic function graph? (Show your work details, or explain how you found the vertex.) 9. What is the equation of the line of symmetry? Explain how you found this equation. 10. Write the vertex form for your quadratic profit function. 11. Is there a maximum profit for your business? If so, how many items must be sold to produce the maximum profit, and what is that maximum profit? If your quadratic profit function has a maximum, show your work or explain how the maximum profit figure was obtained. 12. How would knowing the number of items sold that produces the maximum profit help you to run your business more effectively. 13. Analyze the results of these profit cal.

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The Good, the Bad and the Governed - Why is governance a dirty word? David O'Neill, Chief Operating Officer - APIContext Apidays New York 2024: The API Economy in the AI Era (April 30 & May 1, 2024) ------ Check out our conferences at https://www.apidays.global/ Do you want to sponsor or talk at one of our conferences? https://apidays.typeform.com/to/ILJeAaV8 Learn more on APIscene, the global media made by the community for the community: https://www.apiscene.io Explore the API ecosystem with the API Landscape: https://apilandscape.apiscene.io/

Apidays New York 2024 - The Good, the Bad and the Governed by David O'Neill, ...

apidays

💥 You’re lucky! We’ve found two different (lead) developers that are willing to share their valuable lessons learned about using UiPath Document Understanding! Based on recent implementations in appealing use cases at Partou and SPIE. Don’t expect fancy videos or slide decks, but real and practical experiences that will help you with your own implementations. 📕 Topics that will be addressed: • Training the ML-model by humans: do or don't? • Rule-based versus AI extractors • Tips for finding use cases • How to start 👨‍🏫👨‍💻 Speakers: o Dion Morskieft, RPA Product Owner @Partou o Jack Klein-Schiphorst, Automation Developer @Tacstone Technology

DEV meet-up UiPath Document Understanding May 7 2024 Amsterdam

UiPathCommunity

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