How many cuts can be made on a rope?
Given a rope of length n meters, cut the rope in different parts of integer lengths in a way that maximizes product of lengths of all parts. You must make at least one cut. Assume that the length of rope is more than 2 meters. This problem is similar to Rod Cutting Problem.
What are the V I’s of a rope?
So the V i ‘s are the lengths of the pieces of rope. ( 1 − c 1 − c 2 − … − c k) n − 1. This is proved formally in David and Nagaraja’s Order Statistics, p. 135.
How many cuts must you make to get the maximum product?
You must make at least one cut. Assume that the length of rope is more than 2 meters. This problem is similar to Rod Cutting Problem. We can get the maximum product by making a cut at different positions and comparing the values obtained after a cut.
How do you find the length of a joint pdf?
Break the unit interval at x and y where x < y. Our lengths are then x, y − x, and 1 − y. It’s not hard to show that they all have probability 1 / 3 of being the shortest. In any case, our joint PDF is given by f ( x, y) = 6 (since x and y remain uniform random variables on 1 / 6 th of the square [ 0, 1] × [ 0, 1] ).
How long are the pieces of a 12 foot rope?
A 12 ft rope is cut into three pieces so that the second piece is 1 ft longer than the first and the third piece is 1 ft longer than the second. How long are the pieces? Let the length of the first piece be x. Then according to statement So the three pieces are 3, 4 and 5 ft long. Hope I helped :)!
How long does it take to burn two ropes?
We’re back with another riddle, and this week’s is nice and short, though figuring out the solution can be a bedeviling pursuit. You have two ropes coated in an oil to help them burn. Each rope will take exactly 1 hour to burn all the way through.
What is the length of each strip of rope?
The length of the rope is 5.2 m, which equals 520 cm. 520 cm/20 = 26 cm. So the length of each individual strip would be 26 centimeters.
What is the standard length of a jump rope?
Speed Competition: Length should be no more than 6” inches (.5 ft) between the top of the jumper’s head and the rope as it passes over. Double Unders Competition: Ideal length is 6 – 12 inches (.5ft – 1ft) between the jumper’s head and the rope as it passes over.
What is the cost to connect two ropes of different lengths?
There are given n ropes of different lengths, we need to connect these ropes into one rope. The cost to connect two ropes is equal to the sum of their lengths.
How long is a piece of rope 60 feet?
The whole rope (40 ft) is cut into two pieces. The sum of the lengths of these 2 pieces must total 40 feet. The shorter piece is “x” in length; the longer piece is (10 + 2x). A piece of rope 60 feet long is cut into two pieces. One piece is 12 feet shorter than the other.