Consider the differential equation dy/dx = 3y − 72x.

Find the value of b so that the function

y = 24x + b

is a solution to the differential equation.

Let g be the function that satisfies the differential equation

dy/dx = 3y − 72x

with initial condition

g(0) = 0.

Determine whether the graph of g has a relative minimum, a relative maximum, or neither at the point (0, 0).

George is folding a piece of paper to make an origami figure. each time he folds the paper, the thickness of the paper is doubled. the paper starts out flat, with a thickness of 1 millimeter. a. write a list of six ordered pairs showing the output as the thickness of the paper when the input is the number of times it is folded. explain how you came up with your ordered pairs. b. is this relation a function? explain why or why not using the ordered pairs you came up with in part a.

()1. how do you find range? 2.the following set of data is to be organized into a histogram. if there are to be five intervals on the graph, what should the length of each interval be? 30, 34, 23, 21, 27, 25, 29, 29, 25, 23, 32, 31

Samantha is growing a garden in her back yard. she spend $90 setting up the garden bed and buying the proper garden supplies. in addition, each seed she plants cost $0.25. a. write the function f(x) that represents samantha's total cost on her garden. b. explain what x represents. c. explain what f(x) represents. d. if samantha plants 55 seeds, how much did she spend in total?