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The figure shows a mathematical model for the problem The angle is the angle less the angle Thus we have = = Cot 1 ( x/12) Cot 1 ( x/2) Notice that when the viewer is standing with her face against the wall then = = /2 so that = 0 Also, when the viewer is far from the tapestry then is quite small So the maximum value for will occur for some finite, positive value of x That value can be found by differentiating with respect to x, setting the derivative equal to zero, and solving for x We leave it to you to perform the calculation and discover that 24 ft is the optimal distance at which the viewer should stand

Property int Count { get; } bool IsSynchronized { get; } Meaning The number of items currently held in the collection Is true if the collection is synchronized and false if it is not By default, collections are not synchronized It is possible, though, to obtain a synchronized version of most collections An object upon which the collection can be synchronized

Similarly, You may either select Mary or Jason should be written as You may select either Mary or Jason

object SyncRoot { get; }

Count is the most often used property because it contains the number of elements currently held in a collection If Count is zero, then the collection is empty ICollection defines the following method: void CopyTo(Array array, int index) CopyTo( ) copies the contents of a collection to the array specified by array, beginning at the index specified by index Thus, CopyTo( ) provides a pathway from a collection to a standard C# array Because ICollection inherits IEnumerable, it also includes the sole method defined by IEnumerable: GetEnumerator( ), which is shown here: IEnumerator GetEnumerator( ) It returns the enumerator for the collection Because ICollection implements IEnumerable, four extension methods are defined for it They are AsParallel( ), AsQueryable( ), Cast( ), and OfType( ) AsParallel( ) is declared in SystemLinqParallelEnumerable AsQueryable( ) is declared in SystemLinqQueryable Both Cast( ) and OfType( ) are declared in SystemLinqEnumerable These methods are designed primarily to support LINQ, but may be useful in other contexts

YOU TRY IT Redo the last example if the tapestry is 20 feet high and the bottom of the tapestry is 6 inches above eye level

The IList interface declares the behavior of a non-generic collection that allows elements to be accessed via a zero-based index It inherits ICollection and IEnumerable In addition to the methods defined by ICollection and IEnumerable, IList defines several of its own These are summarized in Table 25-2 Several of these methods imply the modification of a collection If the collection is read-only or of fixed size, then these methods will throw a NotSupportedException Objects are added to an IList collection by calling Add( ) Notice that Add( ) takes an argument of type object Since object is a base class for all types, any type of object can be stored in a non-generic collection This includes the value types, because boxing and unboxing will automatically take place You can remove an element using Remove( ) or RemoveAt( ) Remove( ) removes the specified object RemoveAt( ) removes the object at a specified index To empty the collection, call Clear( ) You can determine whether a collection contains a specific object by calling Contains( ) You can obtain the index of an object by called IndexOf( ) You can insert an element at a specific index by calling Insert( )

25:

Method int Add(object value) void Clear( ) bool Contains(object value) int IndexOf(object value) void Insert(int index, object value) void Remove(object value) void RemoveAt(int index)

Description Adds value into the invoking collection Returns the index at which the object is stored Deletes all elements from the invoking collection Returns true if the invoking collection contains value Returns false if value is not in the collection Returns the index of value if value is contained within the invoking collection If value is not found, 1 is returned Inserts value at the index specified by index Elements at and below index are moved down to make room for value Removes the first occurrence of value from the invoking collection Elements at and below the removed element are moved up to close the gap Removes the object at the index specified by index from the invoking collection Elements at and below index are moved up to close the gap