Problem 1: consider the initial value problem y' + (1/4)y = 3 + 2cos(2t), y(0) = 0. (a) find the solution of this initial value problem and describe its behavior for large t. (b) determine the value of t for which the solution first intersects the line y = 12.
problem 2: find the value of latex: y_0y 0 for which the solution of the initial value problem y' - y = 1+ 3sin(t), y(0) = latex: y_0

In the coordinate plan (-6,9) b (3,9) c (3,3) def is shown in the coordinate plan below

Find the equation of the trend line (line of best fit). show your work i'm using the points (34,76) (42,91)

The table below represents the displacement of a fish from its reef as a function of time: time (hours) x displacement from reef (feet) y 0 4 1 64 2 124 3 184 4 244 part a: what is the y-intercept of the function, and what does this tell you about the fish? (4 points) part b: calculate the average rate of change of the function represented by the table between x = 1 to x = 3 hours, and tell what the average rate represents. (4 points) part c: what would be the domain of the function if the fish continued to swim at this rate until it traveled 724 feet from the reef? (2 points)