Math 110 Final Exam 2 Version 2 12 points each Dec. 12, 2002

1. Distance Formula:

Find the distance between the points (-1, 3) and (4, -5).

2. Equation of a Circle:

Find the equation of the circle with center (3, -1) and Radius 4.

3. Slope of the Line:

Find the Slope of the line between (-2,1) and (3, 4).

4. Slope Intercept:

Find the slope and Y intercept of the line whose equation is 6x &emdash; 2y = 12

5. System of Equations:

Write the system of equations corresponding to the given augmented Matrix:

6. Matrix Equation:

Write the matrix equation that is equivalent to the given system of equations:

x + 4y &emdash; z = 3

2x + 3y &emdash; 2z = 1

-x + 2y + 3z = 7

7.) Adding Matrix:

8.) Graphing Inequalities:

Graph : 2x + y <= 4

9. Find the optimal value(s) of the objective function Z = x + 4y on the feasible set S.

10. Find the accumulated amount A if the principal P is invested at the interest rate r per year for t years when, P = $150,000, r = 12%, t = 3 years, compounded daily.

11.) Future Value

Find amount (future value) of the ordinary annuity: $1800 per quarter for 6 years at 8% per year compounded quarterly.

12. List the elements of the set described:

{x | x is a digit in the number 353,646}

13. Find the set described:

{1,2} ² {1,3,4}²{4,6,8,10}

14. Shade the region A^c _ B

15. Evaluate the expression

3(5!)

16. Evaluate the expression