answers to quiz #2

1.  
    25           ==> 11001
    50           ==> 110010  (multiply by 2 by adding a 0)
    FFFF         ==> 10000(base16) - 1  ===> 65535
    1010101100   ==> 10,1010,1100 ==> 2AC (break into groups of 4 digits)
    1010101100/4 ==> 10101011 (divide by 2 twice by dropping right hand 0s)
    2 x 55F      ==> 55F + 55F ==> ABE
    rank         ==> 8
    suit         ==> 4

2.  One difficulty is how to count the factors.
    For n=1, does that mean x, or x * (1-x^2/pi^2) ?
    Assuming n=1 means the result is x:

    double sinApprox(double x, int n)
    {
        double pi = atan2(1.0, 0.0) * 2.0;
        double result = x;
        int i = 1;
        double term = 0;  // can initialize to anything

        while ( i < n )
        {
            term   = 1 - x*x/(i*i*pi*pi);  // careful with parens
            result = result * term;
            i = i + 1;
        }
        return result;
     }

    If you took "one factor" to mean x * something:

    double sinApprox(double x, int n)
    {
        double pi = atan2(1.0, 0.0) * 2.0;
        double result = x;
        int i = 0;
        double term = 0;  // can initialize to anything

        while ( i < n )
        {
            i = i + 1;
            term   = 1 - x*x/(i*i*pi*pi);  // careful with parens
            result = result * term;
        }
        return result;
     }

3.  
    bool ImPositive(vector<double> x)
    {
       int pos=0, neg=0;
       for (int i=0; i<x.size(), i=i+1)
       {
          if (x[i] < 0)
          {
              neg = neg + 1;
          }
          else if (x[i] > 0) // excluding 0s as neither pos nor neg
          {
              pos = pos + 1;
          }
       }
       return (pos > neg);
     }

     The return line is equivalent to:

       if (pos > neg)
       {
           return true;
       }
       else
       {
           return false;
       }

4.  Note there are various ways to fix this program

#include <iostream>
using namespace std;
int main()
{
int N;                                              <==== moved before cin

cout << "Will calculate Fibonacci(N). Input N: ";   <==== added ;
cin >> N;

                                                    <==== should be N < 1
//if (N > 1)                                        <==== removing line fixes
   {while(N < 1)
      {cout << "F(" << N << ") does not exist. N must be >= 1. Try again." << endl;
      cin >> N;
      }
   }

int F, FMinus1 = 1,FMinus2 = 1;

if (N == 1 || N == 2) //;                           <==== was && (and)
   {F = 1;}                                         <==== also removed ;

else //if                                           <==== removed "if"
   {for (int i = 3; i <= N; i = i + 1)              <==== added "int"
      {F = FMinus2 + FMinus1;
      FMinus2 = FMinus1;                            <==== switched order
      FMinus1 = F;                                  <==== of these two lines
      }
   }

cout << "F(" << N << ") = " << F << endl;           <==== added << before F

return 0;
}

5.  

#include <iostream>
using namespace std;

int main()
{
	double a, b, c;
	cout << " Enter quadratic coefficients a, b, and c " << endl;
	cin >> a >> b >> c;

	double disc = b*b - 4*a*c;
	double r1   = -b/(2*a);

	if (disc == 0)
	{
		cout << " This has one real root at x = " << r1 << endl;
	}
	else if (disc < 0)
	{
		cout << " This has no real roots " << endl;
	}
	else
	{
		double r2 = sqrt(disc) / (2*a);
		cout << " This has two real roots at x = " << r1 + r2
		     << " and at x = " << r1 - r2 << endl;
	}
}