Algorithm complexity The complexity of a computer algorithm is the number of operations or steps the algorithm needs to complete its task assuming there are n pieces of input (for example, the number of steps needed to put n numbers in ascending order). Four algorithms for doing the same task have complexities of A: n 3/2 , B: n log 2 n , C: n (log 2 n ) 2 , and D: n log 2 n . Rank the algorithms in order of increasing efficiency for large values of n . Graph the complexities as they vary with n and comment on your observations.
Algorithm complexity The complexity of a computer algorithm is the number of operations or steps the algorithm needs to complete its task assuming there are n pieces of input (for example, the number of steps needed to put n numbers in ascending order). Four algorithms for doing the same task have complexities of A: n 3/2 , B: n log 2 n , C: n (log 2 n ) 2 , and D: n log 2 n . Rank the algorithms in order of increasing efficiency for large values of n . Graph the complexities as they vary with n and comment on your observations.
Solution Summary: The author explains the ranking order of the algorithms from least to most efficient is A, C, B, D.
Algorithm complexity The complexity of a computer algorithm is the number of operations or steps the algorithm needs to complete its task assuming there are n pieces of input (for example, the number of steps needed to put n numbers in ascending order). Four algorithms for doing the same task have complexities of A: n3/2, B: n log2n, C: n(log2n)2, and D:
n
log
2
n
. Rank the algorithms in order of increasing efficiency for large values of n. Graph the complexities as they vary with n and comment on your observations.
An airplane flies due west at an airspeed of 428 mph. The wind blows in the direction of 41° south of west
at 50 mph. What is the ground speed of the airplane? What is the bearing of the airplane?
428 mph
41°
50 mph
a. The ground speed of the airplane is
b. The bearing of the airplane is
mph.
south of west.
Rylee's car is stuck in the mud. Roman and Shanice come along in a truck to help pull her out. They attach
one end of a tow strap to the front of the car and the other end to the truck's trailer hitch, and the truck
starts to pull. Meanwhile, Roman and Shanice get behind the car and push. The truck generates a
horizontal force of 377 lb on the car. Roman and Shanice are pushing at a slight upward angle and generate
a force of 119 lb on the car. These forces can be represented by vectors, as shown in the figure below. The
angle between these vectors is 20.2°. Find the resultant force (the vector sum), then give its magnitude
and its direction angle from the positive x-axis.
119 lb
20.2°
377 lb
a. The resultant force is
(Tip: omit degree notations from your answers; e.g. enter cos(45) instead of cos(45°))
b. It's magnitude is
lb.
c. It's angle from the positive x-axis is
Find a plane containing the point (3, -3, 1) and the line of intersection of the planes 2x + 3y - 3z = 14
and -3x - y + z = −21.
The equation of the plane is:
Chapter 4 Solutions
Single Variable Calculus: Early Transcendentals Plus MyLab Math with Pearson eText -- Access Card Package (2nd Edition) (Briggs/Cochran/Gillett Calculus 2e)
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