Suppose that d(r) is a function which gives the population density, in hundreds of people per square mile, within r miles of the center of a very small town. assume that there are 100 people per square mile within 5 miles of the town’s center, and 350 people per square mile within 7 miles. a. let t(r) be the number of people (in hundreds) who live within r miles of the city. write an expression for t(r), in terms of r and d(r). b. what is the average rate of change of the function t (r) over the interval [5, 7]

a) T(r) = r.D(r)

b) 975 people per square mile.

Step-by-step explanation:

(a)

The units of D(r) are  

when multiplying the density by the area we get the amount of people in that area, so

(b)

The average rate of change of T(r) over the interval [5,7] is

but D(7) = 350 and D(5) = 100, so

and the average rate of change of T(r) over the interval [5,7] is 975 people per square mile.

9.55 degrees.

step-by-step explanation:

the given angle is

1 cycle is equal to 2π radians. so 4π will be equal to two cycles.

5.166667π-4π = 1.166667π

hence, this angle goes a little more than negative x axis.

1.166667π-π= 0.166667π

hence, the reference angle is 0.166667π radians.

1 radian = 57.2958 degrees

now, in degrees, this should be equals to 9.55 degrees.

answer: all of the odd numbers were opened

the first person was the one that was opening all of the lockers. since one is odd, this causes all of the odd number lockers to be opened in the end.