A major corporation is building a 4325-acre complex of homes, offices, stores, schools, and churches in the rural community of Glen Cove. As a result of this development, the planners have estimated that Glen Cove's population (in thousands) t years from now will be given by:
P(t) = (25t²+125t+200)/(t²+5t+40)
(a) Find the rate at which Glen Cove's population is changing with respect to time.
(b) What will be the population after 10 years? At what rate will the population be increasing when t=10?

(a)

(b)

Step-by-step explanation:

(a) In order to find  the rate at which Glen Cove's population is changing with respect to time we need to calculate the derivative of P(t):

Use the quotient rule:

  (1)

Where:

Replacing into the equation (1) and symplifying:

(b)

In order to find what's the population after 10 years, just evaluate P(t) at t=10

Glen Cove's population is in thousands so:

Finally, to find the rate at which the population is increasing, you need to evaluate the derivative of P(t) at t=10

pentagon

step-by-step explanation:

the coordinates   a(5, -2), b(3,-1),c(-4,-4) d(-3,8) and e(-1,4) forms the vertices of the polygon when they are connected in order.

in order to classify that which polygon is it with the given coordinates, first count the number of vertices and then count the number of sides it can make with these vertices.

since, the given coordinates have five vertices, therefore, it will make five sides. moreover, pentagon is regular in nature therefore it will be convex.

now, a polygon with five sides is known as pentagon, therefore, the given polygon is the pentagon.

10.416 meters per second

step-by-step explanation:

distance=1 00 meters

time= 9.6 seconds in decimal form or 9 3/5 as a mixed number

average speed= 100/9.6

=10.416 meters per second or 10 52/125 as a mixed number.