Fibonacci Numbers.
The Fibonacci numbers are
1,1,2,3,5,8,13,21,….1,1,2,3,5,8,13,21,….
We can define them inductively by f1=1,f1=1, f2=1,f2=1, and...
Fibonacci Numbers.
The Fibonacci numbers are
1,1,2,3,5,8,13,21,….1,1,2,3,5,8,13,21,….
We can define them inductively by f1=1,f1=1, f2=1,f2=1, and
fn+2=fn+1+fnfn+2=fn+1+fn for n∈N.
Prove that fn=[(1+√5)n−(1−√5)n]/2n√5.
The textile mill model -
Produces 3 types of fabric (F1, F2, F3) on 2 types...
The textile mill model -
Produces 3 types of fabric (F1, F2, F3) on 2 types of machines
(Regular, Special). Or Buy.
Time to delivery is 13 weeks.
15 regular machines (F2, F3) + 3 special machines (F1, F2, F3)
+ Buy (F1, F2, F3)
Demand for F1, F2, F3 is 45000, 76500, 10000 yards.
Special loom capacity in yards/hour – 4.7, 5.2, 4.4
Regular loom capacity in yards/hour – 0, 5.2, 4.4
Manufacture cost in $/yard – 0.65, 0.61,...
Given:
function f = fibonacci(n)
% FIBONACCI Fibonacci sequence
% f = FIBONACCI(n) generates the first...
Given:
function f = fibonacci(n)
% FIBONACCI Fibonacci sequence
% f = FIBONACCI(n) generates the first n Fibonacci
numbers.
f = zeros(n,1);
f(1) = 1;
f(2) = 2;
for k = 3:n
f(k) = f(k-1) + f(k-2); end
AND
function f = fibnum(n)
if n <=1
f =1;
else
f = fibnum(n-1) + fibnum(n-2);
end
In Matlab, modify fibonacci.m and fibnum.m to compute
the following sequence.
dn = 0, n<=0
d1 = 1,
d2 = 1
and, for n >...
Determine if the set of functions is linearly independent:
1. f1(x)=cos2x, f2(x)=1, f3(x)=cos^2 x
2. f1(x)=e^...
Determine if the set of functions is linearly independent:
1. f1(x)=cos2x, f2(x)=1, f3(x)=cos^2 x
2. f1(x)=e^ x, f2(x)=e^-x, f3(x)=senhx
Given the vector F1 = 100 N, Ѳ1 = 20o , and F2 = 200 N,...
Given the vector F1 = 100 N, Ѳ1 = 20o , and F2 = 200 N, Ѳ2 = 90o
and F3 = 300 N, Ѳ3 =220o . Find the magnitude and direction of the
resultant F= F1 + F2 + F3 using the following method:
1. Analytical: Use the component method.
2. Graphical: Use the polygon method.
Use a percent error calculation to determine how close the
graphical result are to the analytical method. (1pt.)