Let m be an integer in the set {0,1,2,3,4,5,6,7,8, 9}, and consider the following problem: determine m by asking 3-way questions
, i.e. questions with at most 3 possible answers. For instance, one could ask which of 3 specific subsets m belongs to.
Give a decision tree argument showing that at least 3 such questions are necessary in worst case. In other words, prove that no correct algorithm can solve this problem by asking only 2 questions in worst case.
Give a decision tree argument showing that at least 3 such questions are necessary in worst case. In other words, prove that no correct algorithm can solve this problem by asking only 2 questions in worst case.
1 answer:
Answer:
Take any algorithm if that algorithm solves this problem it can be represented as a ternary decision tree. Therefore each question has at most three answers.
There are ten possible verdicts, the height of such kind of tree should satisfy
ℎ >= ⌈log3(10)⌉ = 3
Hence no such algorithm can ask less than three questions in the worst case.
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b)
Each and every internal node represents a question asking whether m belongs to one of three possible subset of {0, 1, 2, 3, 4, 5, 6, 7, 8, 9} or not
For example 0123|456|789 represented the questionDoes “m: belongs to {0, 1, 2, 3}, to {4, 5, 6}, or to {7, 8, 9}?"
Verdicts are placed in brackets "[ ]"
Explanation:
decision tree is attached below
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Answer:
the volume flow rate per unit depth is:
the ratio is :
Explanation:
From the question; the equations of the velocities profile in the system are:
----- equation (1)
The above boundary condition can now be written as :
At y= 0; u =0 ----- (a)
At y = h; u =0 -----(b)
At y = ; u =
------(c)
where ;
A,B and C are constant
h = distance between two plates
u = velocity
= maximum velocity
y = measured distance upward from the lower plate
Replacing the boundary condition in (a) into equation (1) ; we have:
Replacing the boundary condition (b) in equation (1); we have:
Replacing the boundary condition (c) in equation (1); we have:
replacing for A in (d); we get:
replacing the values of A, B and C into the velocity profile expression; we have:
To determine the volume flow rate; we have:
Replacing
Thus; the volume flow rate per unit depth is:
Consider the discharge ;
Q = VA
where :
A = bh
Q = Vbh
Also;
Then;
Thus; the ratio is :
The net resultant direct force and angle on the vane is created when the water jet exits the vane at position 2 with 92% of its initial velocity.
<h3>What is mean by velocity?</h3>- The speed at which a body or object is moving determines its direction of motion. A scalar quantity, speed is primarily. As a matter of fact, velocity is a vector quantity.
- The rate at which distance changes is what it is. It measures the displacement's rate of change. A body's velocity is defined as its speed in a particular direction.
- Velocity is a measure of how quickly a distance changes in relation to time. Having both magnitude and direction, velocity is a vector quantity.
- The rate of change in a body's displacement with respect to time is referred to as velocity. In the SI, m/s is its unit.
Given,
External angle of Curved Vane = 158°
mean velocity at 1 = 12 m/s
Volumetric flow rate =
mean velocity at
i) Force exerted in x - friction A C 1 = Volume
i
The complete question is:
A horizontal jet of water strikes a curved vane as shown in Figure C.1. The external angle of the curved vane is 158°.The mean velocity and volumetric flow rate of the water jet at position 1 are 12 m/s and 55 m³/h respectively. Due to friction, the water jet leaves the vane at position 2 with 92 % its original velocity.
(i) Direct force exerted by the water jet on the vane in the x - direction.
(ii) Direct force exerted by the water jet on the vane in the y - direction.
(ii) Net resultant direct force and angle on the vane.
To learn more about velocity, refer to:
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