Problems 61-70 refer to the following transition matrix P and its powers A B C P = A B C .6 .3 .1 .2 .5 .3 .1 .2 .7 A B C P 2 = A B C .43 .35 .22 .25 .37 .38 .17 .27 .56 A B C P 3 = A B C .35 .348 .302 .262 .336 .402 .212 .298 .49 Using a graphing calculator to compute powers of P , find the smallest positive integer n such that the corresponding entries in P n and P n + 1 are equal when rounded to two decimal places.
Problems 61-70 refer to the following transition matrix P and its powers A B C P = A B C .6 .3 .1 .2 .5 .3 .1 .2 .7 A B C P 2 = A B C .43 .35 .22 .25 .37 .38 .17 .27 .56 A B C P 3 = A B C .35 .348 .302 .262 .336 .402 .212 .298 .49 Using a graphing calculator to compute powers of P , find the smallest positive integer n such that the corresponding entries in P n and P n + 1 are equal when rounded to two decimal places.
Solution Summary: The author calculates the smallest positive integer n, which equals when rounded off to two decimal places, using graphing calculator.
Problems 61-70 refer to the following transition matrix
P
and its powers
A
B
C
P
=
A
B
C
.6
.3
.1
.2
.5
.3
.1
.2
.7
A
B
C
P
2
=
A
B
C
.43
.35
.22
.25
.37
.38
.17
.27
.56
A
B
C
P
3
=
A
B
C
.35
.348
.302
.262
.336
.402
.212
.298
.49
Using a graphing calculator to compute powers of
P
, find the smallest positive integer
n
such that the corresponding entries in
P
n
and
P
n
+
1
are equal when rounded to two decimal places.
Function: y=xsinx
Interval: [ 0 ; π ]
Requirements:
Draw the graphical form of the function.
Show the coordinate axes (x and y).
Choose the scale yourself and show it in the flowchart.
Create a flowchart based on the algorithm.
Write the program code in Python.
Additional requirements:
Each stage must be clearly shown in the flowchart.
The program must plot the graph and save it in PNG format.
Write the code in a modular way (functions and main section should be separate).
Expected results:
The graph of y=xsinx will be plotted in the interval [ 0 ; π ].
The algorithm and flowchart will be understandable and complete.
When you test the code, a graph file in PNG format will be created.
A company specializing in lubrication products for vintage motors produce two
blended oils, Smaza and Nefkov. They make a profit of K5,000.00 per litre of
Smaza and K4,000.00 per litre of Nefkov. A litre of Smaza requires 0.4 litres of
heavy oil and 0.6 litres of light oil. A litre of Nefkov requires 0.8 litres of heavy oil
and 0.2 litres of light oil. The company has 100 litres of heavy oil and 80 litres of
light oil. How many litres of each product should they make to maximize profits
and what level of profit will they obtain? Show all your workings.
Use the graphs to find estimates for the solutions of the simultaneous equations.
Chapter 9 Solutions
Finite Mathematics for Business, Economics, Life Sciences and Social Sciences
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