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

Answer: d. 39 cmin the diagram, the approximate length of the minor arc de is 39 centimetres.step-by-step explanation: the formula for the length of an arc in a circle is as displayed below.let the length of the minor arc de = xx = 2( pi )r × angle of sector / 360°from this, we will substitute the values given from the problem into the formula to obtain the length of the minor arc de.x = 2( pi )r × angle of sector / 360°r = radius = 25cmpi as an approximate value = 3.14angle of sector = 120°x = 2( 3.14 )( 25 ) × 120° / 360°x = 157 × 1 / 4x = 39.25x = 39 ( rounded to the nearest whole number as an approximate value )