Write a method called perfectNumbers that accepts an integer maximum as its parameter and returns a String containing all "perfect numbers" up to and including that maximum. (The String should be formatted such that the perfect numbers are listed in increasing order and separated by a space.) The call perfectNumbers(500); should produce the following String: "6 28 496". You should use isPerfectNumber within this method. If a non-positive number is given to perfectNumbers, an IllegalArgumentException should be thrown.

In a heat transfer course, we can derive the equation for the temperature distribution in a flat rectangular plate. in this example, we will look at a plate at steadystate with three sides being held at t1, and one side held at t2. the temperature for any location on the plate, t(x,y), can be calculated by where create a function (prob3_5) that will take inputs of vectors x and y in feet, scalar n, scalars l and w in feet and scalars t1 and t2 in degrees fahrenheit. it will output a matrix t which is the temperature of each x and y locations. t will have the number of columns equal to the number of elements in x and rows equal to the number of elements in y. though this can be done without loops (perhaps more efficiently), your program must use a nested loop.