5. Exercise Set 1

Exercise 1.1: The Circle

Given: a real value, r, for the radius of a circle;
Compose: a let-in statement that returns the area and circumference of a circle of the given radius.
Click here for a sample answer.

Exercise 1.2: Statistics

Given: four values, a, b, c, and d, all real numbers;
       the formulas for the mean and standard deviation
            mean = (a+b+c+d)/4;
            standard deviation = (((a-mean)**2 + (b-mean)**2 +
                                   (c-mean)**2 + (d-mean)**2) / 3)**0.5

Compose: a let-in statement that returns the mean and standard deviation of the given set of numbers.
Click here for a sample answer.

Exercise 1.3: Cubic Roots

Given: two real values, a, and  b, coefficients of the cubic
            equation x**3 + ax + b = 0;

       the formulas for the roots x = C + D,
                                      -(C + D)/2 + 3**0.5*(C - D)/2, and
                                      -(C + D)/2 - 3**0.5*(C - D)/2,
            where C = (-b/2 + ((b**2)/4 + (a**3)/27)**0.5)**(1/3), and
                  D = (-b/2 + ((b**2)/4 - (a**3)/27)**0.5)**(1/3);

Compose: a let-in statement that returns the roots of the cubic equation.
Click here for a sample answer.

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John Feo at (510) 422-6389 or feo@diego.llnl.gov, or Tom DeBoni at (510) 423-3793 or deboni@llnl.gov.

The Sisal Language Project has been approved as a Designated Unclassified Subject Area (DUSA) K19222, as of 07 August, 1991.