Sudoku is just a puzzle, but the backtracking technique for solving it is used in many important application domains. To solve a Sudoku without backtracking, you could generate every possible solution, then evaluate all of them and collect the legal ones. But there are 9^81 ways to fill in a Sudoku grid. 9^81 is ~= 2*10^77. If you could evaluate a billion grids per second, it would take 2*10^68 seconds. The universe is less than 10^18 seconds old. For this homework, you will learn the power of backtracking by writing a Sudoku solver that finds answers in just a few seconds.

1.4

2.3

step-by-step explanation:

the formula for the constant of variation is

y= kx

divide each side by x

y/x =kx/x

y/x =k

we know a and y

1.   y/x = k

4/1 =4

check the other values to make sure they are the same

8/2 = 4   12/3 =4   and 16/4 =4  

the constant of variation is 4

2.   y/x = k

3/1 =3

check the other values to make sure they are the same

6/2 = 3   9/3 =3   and 12/4 =3  

the constant of variation is 3

1 number

if we use a graphing calculator, there is only one such number that satisfies the conclusion of the mean value theorem, that is, a number such that

where the right-hand side is the average rate of change of f on the interval [0.5,0.75], which is the slope of the secant line.

in the attached graph, the black line is the secant line which has its slope as the average rate of change of f on [0.5,0.75], while the orange line is the only tangent line to the graph of f in the interval that satisfies the mvt conclusion.