The given family of functions is the general solution of the differential equation on the indicated interval. Find a member of the family that is a solution of the initial-value problem. y = c1e4x + c2e−x, (−[infinity], [infinity]); y'' − 3y' − 4y = 0, y(0) = 1, y'(0) = 1

Plz need answer now will mark which situations represent linear functions? check all that apply. a)the temperature rises and falls over the course of a day. temperature is a function of time. b)a baseball is hit into the outfield. the height of the ball is a function of time. c)a car goes 55 mph on the highway. distance is a function of time. d)a child grew 2 inches this year and 1 inch last year. height is a function of time. e)a movie director makes 2 movies per year. the number of movies is a function of the years.

The number of branches on a tree demonstrates the fibonacci sequence. how many branches would there be on the next two levels of this tree? 13 | | | m branches

In right ∆abc shown below, the midpoint of hypotenuse ac is located at d and segment bd is drawn.if ab = 12 and bc = 16, then explain why bd = 10. hint: consider what you know about the diagonals of a rectangle.