Following the lead of the national wildlife federation, the department of the interior of a south american country began to record an index of environmental quality that measured progress and decline in the environmental quality of its forests. the index for the years 2004 through 2014 is approximated by the functioni i(t) = 1/3t^3 − 5/2t^2 + 80 (0 ≤ t ≤ 10) where t = 0 corresponds to 2004. for what years is the quality of the forests in this country improving?

After 2009 the quality of the forests in this country improving.

Step-by-step explanation:

Consider the provided function.

Substitute f'(t)=0.

It is given that  (0 ≤ t ≤ 10)

The test interval are (0,5) and (5,10)

For (0 < t < 5) the value of

For (5 < t < 10) the value of

Hence, the function is increasing from (5,10).

t = 0 corresponds to 2004.

Therefore, after 2009 the quality of the forests in this country improving.

the answer would be d.

step-by-step explanation:

move all variables to the left side and all constants to the right side

(x−3)^2+(y−1)^2=16

this is the form of a circle. use this form to determine the center and radius of the circle.

( x − h ) 2 + ( y − k ) 2 = r 2

match the values in this circle to those of the standard form. the variable   r   represents the radius of the circle,   h   represents the x-offset from the origin, and   k   represents the y-offset from origin.

r = 4

h = 3

k = 1

the center of the circle is found at   ( h , k ) .

center:   ( 3 , 1 )

these values represent the important values for graphing and analyzing a circle.

center:   ( 3 , 1 ).

radius:   4