A city along the edge of a river is semi-circular shaped with a radius 16 miles. In each case below, determine the shape of the strip that would be appropriate for the given population density. Then write a definite integral to represent the total population in the city.

(a) The population density is p(x) = -20x + 500 people per square mile where x is the distance in miles from the center of the city.

(b) The population density is p(x) = 175 people per square mile where x is the vertical distance in miles from the river.

In the diagram, ab is tangent to c, ab = 4 inches, and ad = 2 inches. find the radius of the circle.

What is the value of x? enter your answer in the box.

Have you ever been in the middle of telling a story and had to use hand gestures or even a drawing to make your point? in algebra, if we want to illustrate or visualize a key feature of a function, sometimes we have to write the function in a different form—such as a table, graph, or equation—to determine the specific key feature we’re looking for. think about interactions with others and situations you’ve come across in your own life. how have you had to adjust or change the way you represented something based on either the concept you were trying to describe or the person you were interacting with? explain how the complexity or layout of the concept required you to change your style or presentation, or how the person’s unique learning style affected the way you presented the information.