Consider the following variant of Buffon's needle problem (Example 3.1 1) ' which was investigated by Laplace. A needle of length I is dropped on a plane surface that is partitioned in rectangles by horizontal lines that are a apart and vertical lines that are b apart. Suppose that the needle's length I satisfies 1 < a and 1 < b. What is the expected number of rectangle sides crossed by the needle?

the required function is .

step-by-step explanation:

from the given table it is noticed that the graph passing through (-3,7), (0,4), (3,1) and (8,-4).

it is a linear function because the value of y is decrease by one as the value of x increase by 1.

the slope of the function is

the slope of the function is -1 and the y-intercept is 4.

the slope intercept form is

where, m is slope and b is y-intercept.

therefore the required function is . the graph of this function is shown below.

is there supposed to be a picture here?