Calculating Probability of Golf Ball Landing Near Hole on 4th Hole

[woodworker101]

I have a word problem and then a finite difference problem.

You are playing golf on the 4th hole of your favorite course. The green on this hole is circular with a radius of 20 yards. If the hole is located at the exact center of the green, what is the probablility that the ball will randomly fall within 2 feet of the center of the hole?

finding Finite differences - nth order differences

f(x) = 2x^2 -5x^2 -x

I don't know how to start it and how to get the answer. Thanks for the help.

 

[Moo Of Doom]

Assuming the ball will always land on the green, just find the area of the green and the area of the 2-foot circle, then compare them (in a ratio). (Remember to keep your units consistent).

 

[woodworker101]

I got 900 to 1. Is the correct or even close.

 

[HallsofIvy]

Yes. Actually, you don't even need to calculate the areas themselves to compare them. The hole has radius 2 feet and the green 60 feet- a ratio of 1 to 30. Since area depends on the square of linear distance the area will have ratio 1 to 900.
The probability that a ball that lands randomly on the green will land in the hole is 1/900.

As for f(x) = 2x^2 -5x^2 -x, I see a function (although I would write f(x)=
-3x^2- x) but I see no finites differences and I certainly don't see a question!
What is the problem?

 

[woodworker101]

The question is for the finite difference is: Show that the nth-order differences for the given function of deghree N are nonzero and constant. such as f(x) = 2x^3 - 5x^2 - x

 

[woodworker101]

I am curious how you got ur 900 to 1 ratio. Would the probably also be 1 % too.