Answer to Question #262435 in Math for matt

Question

a)              Solve the following equation:         

log (5x- 11)=2                                       

b)             Change to base 10 and arrange in descending order:  1111₂, 1001₂, 11001₂.

c)             Given x = {a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t},  

            P = {b, e, c, j, l, m, o, n}, R = {c, i, k, m, n, o, s} and S= {c, e, k, n, q, r, t}. 

 

            Determine the following (all work must be shown):

               i.           (P È S)¢

               ii.           (P È R È S)¢

              iii.           (P È S)¢Ç (P È R)

               iv.           [(P È R) Ç (PÇ S)] È (P È R)¢  

d) Briefly explain the concept of gradient with appropriate examples.                       

e)  If one line has a slope of 3 and another has a slope of -6, which line is less steep? Why?

 f)  Given the two points M(3, -5) and N(-2, 6) find the midpoint, length and gradient of MN.                                                                                                                                   g)  Find the equation of the line that passes through the point (-1, -4) and is

 perpendicular to the line x - 3y = 6.  Graph the lines for the equations in (d) on the same axes.