We also discussed the use of the Extended Euclidian algorithm
to calculate modular inverses. Use this algorithm to compute the
following values. Show all of the steps involved.
9570-1(mod 12935)
550-1 (mod 1769)
Exercise 4.9.29: Solve the following systems of congruences, or
state that there is no solution. Be sure to state if there are
multiple solutions.
a. {6 = 13a + b(mod 26), 13 = 4a + b(mod 26)
b. {14 = 17a + b(mod 26), 8 = 7a + b(mod 26)
c. {1 = 15a + b(mod 26), 10 = 9a + b(mod 26)
Please solve the recurrence relation by finding the explicit
formula of each problem. Show all work, thanks!
A. ck = 6ck-1 -
9ck-2 k≥2,
c0 =1, c1=3
B. dk = 2dk-1 +k
k≥1, d0 =1, d1=3
C. ak = 3ak-1 +
2
k≥1, a0 =3
D. bk = -bk-1 + 7bk-2
k≥2, b0 =1,
b1=4
Show the differential equation is not exact and by finding an
appropriate integrating factor solve the given initial problem.
(yx+y^2+ y) dx + (x+2y) dy =0
Solve the given initial-value problem by finding, as in Example
4 of Section 2.4, an appropriate integrating factor.
(x2 + y2 ? 3)
dx = (y + xy)
dy, y(0) = 1
Given the function f(x) on the right solve the following root
finding questions: a) Find a positive root (x > 0) of f(x) using
the Bisection Method
. b) Find a negative root (x < 0) of f(x) using the Bisection
Method.
c) Find a positive root (x > 0) of f(x) using the False
Position Method.
d) Find a negative root (x < 0) of f(x) using the False
Position Method. Find your initial Bracket via Trial-and-Error. Use
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