Q b)
Lines are intersecting at point (5, 3)
Q C)
Lines are parallel no intersecting point.
Q e)
Lines are intersecting at point (0, 0)
Q f)
Lines are intersecting at point (-1, 2)
ALGEBRA
Q1. A culture of bacteria originally numbers 500. After 2 hours there are 1500 bacteria in the culture.
Assuming exponential growth, how many are there after 6 hours?
Solution:
Let the function f(t) measure the bacteria at the time t we have
F(t)
Q1: Compute the average value of
f (x, y) = x2 +y2 over R = cfw_ (x, y) 0 x 2, 0 y 2 .
Ans: the average value of the function f(x, y) is
[1/A(R)
f (x , y )
dA] over the given region
2
x +
( y 2 )
[
2
dx.dy =
0
2
1
2
0
8
2
[ + 2 y ]
3
2
=
=
1
20
x3
+ y 2
The given equation is:
Cos(pi/11)* Cos(2pi/11)* Cos(3pi/11)* Cos(4pi/11)* Cos(5pi/11)
Multiplied and divide the given Expression by 2 sin(pi/11)
[2cos
sin
( 11pi )sin ( 11pi )]cos ( 211pi )cos ( 311pi )cos( 411pi )cos ( 511pi )
pi
2sin ( )
11
( 211pi )cos
1. Consider the following matrix:
1.7 0.3
A
1.2 0.8
Classify the origin as an attractor, repellor, or saddle point of the dynamical system
. Find the direction of greatest attraction and /or repulsion.
x k 1 Ax k
Solution:
Any matrix satisfies its char