## 5. Exercise Set 1

Note: The exponentiation operation "`a**b`" as described below does not exist in Sisal-1.2. Use instead "`exp(a,b)`". The normal exponential function is "`etothe(b)`". Since this is an external function, a "global" declaration is required:
`global etothe(b: real returns real)`

or
`global etothe(b: double_real returns double_real)`

Also, since integers and reals cannot be mixed in Sisal, expressions like "`a/4`" where "`a`" is real are illegal. Use "`a/4.0`" instead.
-- D. J. Raymond, 17 Jan 2015.

#### 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.