Count the number of ordered tuples in the following relations. show your work. (a) the 3-ary relation c is a subset of the cartesian product of {1, 2, 3, 4} × {1, 2, 3, 4} × {1, 2, 3, 4} and is the set of ordered tuples < c1, c2, c3 > such that c1 and c2 are two distinct digits between 1 and 4 inclusive, and c2 and c3 are two distinct digits between 1 and 4 inclusive. (b) the 3-ary relation b is a subset of the cartesian product of {1, 2, 3, 4, 5, 6, 7, 8, 9}×{1, 2, 3, 4, 5, 6, 7, 8, 9}× {1, 2, 3, 4, 5, 6, 7, 8, 9} and is the set of ordered tuples < b1, b2, b3 > such that b1, b2, and b3 are distinct integers between 1 and 9 inclusive, where at least one of the three is even and at least one of the three is odd.

Consider the following statements: #include #include class temporary { private: string description; double first; double second; public: temporary(string = "", double = 0.0, double = 0.0); void set(string, double, double); double manipulate(); void get(string& , double& , double& ); void setdescription(string); void setfirst(double); void setsecond(double); }; write the definition of the member function set() so that the instance variables are set according to the parameters. write the definition of the constructor so that it initializes the instance variables using the function set() write the definition of the member function manipulate() that returns a decimal number (double) as follows: if the value of description is "rectangle", it returns first * second if the value of description is "circle" it returns the area of a circle with radius first if the value of description is "cylinder" it returns the volume of a cylinder with radius first and height second. hint: the volume of a cylinder is simply the area of the circle at the base times the height. if the value of description is "sphere" it returns the volume of the sphere with radius first. otherwise it returns -1.0;

Using least squares fitting, you are to fit the data sets to the following models and solve for the parameters ai , where i is the index of the parameter. the input/output data for the systems are linked in the bblearn site. for each of the systems use matlab to plot the supplied data vs. the model fit on one plot. include your code in the solutions. (a) linear fit "lineardata. mat" y=a1x^3 + a2x^2 + a3x + a4 (b) plant fit "plantdata. mat g(s) = a1/(s + a2)

Which tab should you open to find the option for adding a header?