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// Constructor for TwoDShape public TwoDShape(double w, double h) { Width = w; Height = h; } // Properties for Width and Height public double Width { get { return pri_width; } set { pri_width = value < 0 -value : value; } } public double Height { get { return pri_height; } set { pri_height = value < 0 -value : value; } } public void ShowDim() { ConsoleWriteLine("Width and height are " + Width + " and " + Height); } } // A derived class of TwoDShape for triangles class Triangle : TwoDShape { string Style; // Call the base class constructor public Triangle(string s, double w, double h) : base(w, h) { Style = s; } // Return area of triangle public double Area() { return Width * Height / 2; } // Display a triangle's style public void ShowStyle() { ConsoleWriteLine("Triangle is " + Style); } } class Shapes4 { static void Main() { Triangle t1 = new Triangle("isosceles", 40, 40); Triangle t2 = new Triangle("right", 80, 120); ConsoleWriteLine("Info for t1: "); t1ShowStyle(); t1ShowDim(); ConsoleWriteLine("Area is " + t1Area());

Part I:

SOLUTION If x > 0 then ln x ln x = = ln x ln e 1 Thus we see that the natural logarithm ln x is precisely the same as loge x loge x = Math Note: In mathematics, it is common to write ln x rather than loge x You Try It: Calculate log3 27 + log5 (1/25) log2 8

ConsoleWriteLine(); ConsoleWriteLine("Info for t2: "); t2ShowStyle(); t2ShowDim(); ConsoleWriteLine("Area is " + t2Area()); } }

public Triangle(string s, double w, double h) : base(w, h) {

Substituting in Equations B-1 and B-2, VSWR |V | |V | _____________ |V | |V | (B-3)

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In this version, Triangle( ) calls base with the parameters w and h This causes the TwoDShape( ) constructor to be called, which initializes Width and Height using these values Triangle no longer initializes these values itself It need only initialize the value unique to it: Style This leaves TwoDShape free to construct its subobject in any manner that it chooses Furthermore, TwoDShape can add functionality about which existing derived classes have no knowledge, thus preventing existing code from breaking Any form of constructor defined by the base class can be called by base The constructor executed will be the one that matches the arguments For example, here are expanded versions of both TwoDShape and Triangle that include default constructors and constructors that take one argument

// Add more constructors to TwoDShape using System; class TwoDShape { double pri_width; double pri_height; // Default constructor public TwoDShape() { Width = Height = 00; } // Constructor for TwoDShape public TwoDShape(double w, double h) { Width = w; Height = h; } // Construct object with equal width and height public TwoDShape(double x) { Width = Height = x; } // Properties for Width and Height public double Width { get { return pri_width; } set { pri_width = value < 0 -value : value; } }

We will be able to do calculations much more easily if we learn some simple properties of logarithms and exponentials If a > 0 and b > 0 then a (loga b) = b If a > 0 and b R is arbitrary then loga (a b ) = b If a > 0, b > 0, and c > 0 then (i) loga (b c) = loga b + loga c (ii) loga (b/c) = loga b loga c logc b (iii) loga b = logc a 1 (iv) loga b = logb a (v) loga 1 = 0 (vi) loga a = 1 (vii) For any exponent , loga (b ) = (loga b) We next give several examples to familiarize you with logarithmic and exponential operations EXAMPLE 621

11:

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