In this problem we use the change of variables x=5s+tx=5s+t, y=s−ty=s−t to compute the integral ∫r(x+y)da∫r(x+y)da, where rr is the parallelogram with vertices (x, y)=(0,0)(x, y)=(0,0), (5,1)(5,1), (6,0)(6,0), and (1,−1)(1,−1).

The Jacobian matrix for this transformation is

The vertices in the plane correspond to the following points in the plane:

That is, the parallelogram is mapped to a square in the plane, so

e^-kt = n/n0 = 0.79  

-kt = ln 0.79  

t = - ln 0.79/0.0001  

= 2357 years

step-by-step explanation:

system of linear equation

step-by-step explanation:

as given in the data

a= 20 , b= -12

let us suppose that it is a straight line equation

now we know the formula for the system of linear equation

b= ma + c )

here m is slope of a straight line which is equal to formula

m=   (ii)

and here c is a constant

now putting the value of a and b in equation (ii)

m=

m=

putting the value of a,b and m in equation (i) gives us

-12 = + c

-12=-12 + c

adding 12 to both sides

-12 +12 = -12 +12 +c

0 =c

or c=0

as the value of the constant is zero which gives us that it is a linear equation and this order pair satisfies the system of linear equations.