School

York UniversityDepartment

Information TechnologyCourse Code

ITEC 2600Professor

Xiaofeng ZhouStudy Guide

QuizThis

**preview**shows half of the first page. to view the full**2 pages of the document.**ITEC2600 Winter2018 X.Zhou York University

ITEC 2600

Introduction to Analytical Programming

Lab Exercise ♯8

1. Redo all examples from the lecture.

2. Write a function that will receive a variable number of input arguments: the semi-major axe(a) and semi-

minor axe (b) of a ellipse, and possibly also the height(h) of elliptic cylinder that has this ellipse as its

base. The function should return the ellipse area if just the length and width are passed(area =π×a×b),

or also the volume(v=π×a×b×h) if the height is also passed.

3. Probelm 7 from Textbook: An Introduction with Application, page 87.

The remaining loan balance, B, of a ﬁxed payment nyears mortgage after xyears is given by:

B=L[(1 + r

12 )12n−(1 + r

12 )12x]

(1 + r

12 )12n−1

where Lis the loan amount, and ris the annual interest rate. Calculate the balance of a 30-year,

✩100,000 mortgage, with annual interest rate of 6% (use 0.06 in the equation) after 0, 5, 10, 15, 20, 25,

and 30 years. Create a seven-element vector for xand use element-by-element operations. Display the

results in a two-row table where the values of years and balance are displayed in the ﬁrst and second

rows, respectively.

Write a user-deﬁned function to implement above. Use the variable number of input/output to make

this user-deﬁned function more general. For example, a customer want to know diﬀerence of borrowing

✩200,000 at interest rate 5% and %6, or can customer aﬀord ✩200,000 loan or ✩250,000 loan? Write a

script ﬁle to help customer make smart decision.

4. πapproximation

(a) Figure below shows a circle with radius r= 1 inscribed within a square.

(b) The area of the circle is πr2=π, the area of the square is (2r) = 4. The ratio of two areas can be

represented as

ratio =Area of circle

Area of square =π

4

(c) Generate a random point(x, y), where −1<=x;y <= 1, we can estimate the ratio by checking the

random points falls in the which area as follows:

ratio =Number of points fall in circle

T he total number of pints f alls in square

1

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