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SOLUTION Let h(t) be the height of the ladder at time t and b(t) be the distance of the base of the ladder to the wall at time t Then the Pythagorean theorem tells us that h(t)2 + b(t)2 = 132 We may differentiate both sides of this equation with respect to the variable t (which is time in minutes) to obtain 2 h(t) h (t) + 2 b(t) b (t) = 0 Solving for h (t) yields h (t) = b(t) b (t) h(t)

// A simple generic delegate using System; // Declare a generic delegate delegate T SomeOp<T>(T v); class GenDelegateDemo { // Return the summation of the argument static int Sum(int v) { int result = 0; for(int i=v; i>0; i--)

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TABLE B3 K Cv Ca 00000 -05110 -10163 -15105 -19882 -24440 91 92 93 94 95 090370 091153 091900 092614 093294 093939 094555 095136 095679 096187 96 97 98 99 100 -28731 -32708 -36326 -39546 -42333 09593 09185 08778 08371 07963 07556 07149 06741 06334 05927 90 089549 10000 20000 19979 19915 19810 19664 19479 19257 19001 18713 18396 18055 010451 011300 012181 013100 014053 015036 016057 017113 018203 019323 020471 12444 12851 13259 13666 14073 48881 48881 48881 48881 48881 66 67 68 69 70 059873 061467 063036 064586 066101 10407 10815 11222 11629 12037 48881 48881 48881 48881 48881 61 62 63 64 65 051667 053328 054985 056623 058255 10000 48881 60 050000 Cv Ca Pt K Cv K Pt Ca -48881 -48881 -48881 -48881 -48881 -48881 -48881 -48881 -48881 -48881 -48881

Part I:

result += i; return result; } // Return a string containing the reverse of the argument static string Reflect(string str) { string result = ""; foreach(char ch in str) result = ch + result; return result; } static void Main() { // Construct an int delegate SomeOp<int> intDel = Sum; ConsoleWriteLine(intDel(3)); // Construct a string delegate SomeOp<string> strDel = Reflect; ConsoleWriteLine(strDel("Hello")); } }

1 2 3 4 5

The output is shown here:

At the instant the problem is posed, b(t) = 5, h(t) = 12 (by the Pythagorean theorem), and b (t) = 1 Substituting these values into the equation yields 5 1 5 = ft/min 12 12 Observe that the answer is negative, which is appropriate since the top of the ladder is falling h (t) = You Try It: Suppose that a square sheet of aluminum is placed in the hot sun It begins to expand very slowly so that its diagonal is increasing at the rate of 1 millimeter per minute At the moment that the diagonal is 100 millimeters, at what rate is the area increasing EXAMPLE 313

Let s look closely at this program First, notice how the SomeOp delegate is declared:

000001 000005 000016 000037 000073

delegate T SomeOp<T>(T v);

Notice that T can be used as the return type even though the type parameter T is specified after the name SomeOp Inside GenDelegateDemo, the methods Sum( ) and Reflect( ) are declared, as shown here:

A sponge is in the shape of a right circular cone (Fig 316) As it soaks up water, it grows in size At a certain moment, the height equals 6 inches, and is increasing at the rate of 03 inches per second At that same moment, the radius is 4 inches, and is increasing at the rate of 02 inches per second How is the volume changing at that time

00021 00085 00190 00336 00521

static int Sum(int v) { static string Reflect(string str) {

The Sum( ) method returns the summation of the integer value passed as an argument The Reflect( ) method returns a string that is the reverse of the string passed as an argument Inside Main( ), a delegate called intDel is instantiated and assigned a reference to Sum( ):

05110 10163 15105 19882 24440

SomeOp<int> intDel = Sum;

SOLUTION We know that the volume V of a right circular cone is related to the height h and the radius r by the formula 1 V = r 2 h 3 Differentiating both sides with respect to the variable t (for time in seconds) yields dV 1 dr dh = 2r h + r 2 dt 3 dt dt

Because Sum( ) takes an int argument and returns an int value, Sum( ) is compatible with an int instance of SomeOp

18:

31 32 33 34 35

In similar fashion, the delegate strDel is created and assigned a reference to Reflect( ):

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