Approximate the solution to the equation above using three iterations of successive approximation. use the graph below as a starting point.

  x ≈ 1.683006

Step-by-step explanation:

There are many successive approximation techniques. For these functions, it seems to work to solve the equation for x:

  6^(-x) +4 = 3x -1

  6^(-x) +5 = 3x . . . . . . add 1

  (6^(-x) +5)/3 = x . . . .  divide by the coefficient of x

Then we can use the function ...

  f(x) = (6^(-x) +5)/3

to find a new value of x, given an initial value of x.

As we read the graph, the point where the curves cross is at about x=1.7, so that will be our initial starting point for iteration. The attachment shows the successive values of f(x) for three iterations. The third evaluation of f(x) gives an approximate root value of ...

  x ≈ 1.683006

complete the steps to find the area of the trapezoid.

area of rectangle = 256   square units

area of triangle 1 = 24  square units

area of triangle 2 = 16  square units

area of triangle 3 =   96 square units

area of trapezoid = 120  square units

step-by-step explanation:

x is the total time in minutes for the free response

you are given number of questions as 15 - m and time per item as 8 minutes

to find x multiply the two givens together:

x = 8 * (15-m) = 8(15-m)