We will find the solution to the following lhcc recurrence:
an=−2an−1+3an−2 for n≥2 with initial conditions a0=4,a1=7
the first step in any problem like this is to find the characteristic equation by trying a solution of the "geometric" format an=rnan=rn. (we assume also r≠0). in this case we get:
r^(n)=−2r^(n−1)+3r^(n−2.)
since we are assuming r≠0 we can divide by the smallest power of r, i. e., r^(n−2) to get the characteristic equation:
r^(2)=−2r+3
(notice since our lhcc recurrence was degree 2, the characteristic equation is degree 2.)
find the two roots of the characteristic equation r1 and r2. when entering your answers use r1≤ r2:
r1=
r2=

Step-by-step explanation:

In standard form, the characteristic equation is ...

  r^2 +2r -3 = 0

This factors as ...

  (r +3)(r -1) = 0

and has roots -3 and 1. In your format, ...

  r1 = -3

  r2 = 1

answer: f = 32.2m

step-by-step explanation: that is the answer

the system of inequalities is

step-by-step explanation:

step 1

find the equation of the dashed line

we have the points

(0,0) and (3,1)

the line passes through the origin, so, is a direct variation

find the slope

the equation of the dashed line is

the solution of the inequality a s the shaded area above the dashed line

therefore

the equation of the inequality a is

step 2

find the equation of the solid line

we have the points

(4,0) and (0,4)

find the slope

the equation of the solid line is

the solution of the inequality b s the shaded area below the solid line

therefore

the equation of the inequality b is

step 3

the system of inequalities is