Ahorizontal plane is ruled with parallel lines 5 inches apart. a five inch needle is tossed randomly onto the plane. the probability that the needle will touch a line is given below,
p = 2/π ∫π/2 0 sinθ dθ
where θ is the acute angle between the needle and any one of the parallel lines.
1. find this probability. (round your answer to one decimal place.)

0.6

Step-by-step explanation:

To get the probability P, we need to evaluate the definite integral given.

P = 2/π ∫π/2 0 sinθ dθ

Integration of sinθ is -cosθ

P = 2/Π{-cosθ}... (1)

Substituting the upper limit of the integral which is Π/2 into equation 1;

P1 = 2/Π{-cosΠ/2}

P1 = 2/Π{0} since cosΠ/2 is "zero"

Similarly substituting the value at the lower limit which is "zero" into equation (1)

P2 = 2/Π{-cos0}

P2 = 2/Π{-1} since cos0 is 1

P2 = -2/Π

The probability P will be equal to P2-P1 {upper limit value - lower limit value}

P = 0-(-2/Π)

P = 2/Π

P = 0.6 ( to 1d.p)

f(x) = x^3 -2x^2 -3x

x( x^2 -2x-3)

x( x^2 +x -3x -3)

x( x(x+1) -3(x+1))

x( x-3)( x+1)

so zeroes are 0, 3,-1

its (2) option

hope this is what you were asking for!

step-by-step explanation: