4. you are planning to buy a new couch for your family room. before you leave for the furniture store, you measure the available space and conclude that the couch should be between 5’ - 10” and 6’ - 8” long. at the store you find a couch that you like. the specification sheet on the couch indicates that that the couch is 78 inches long.

a. what are the limits on the couch length in inches?

b. what is the length of the couch in feet and inches? hint: convert the measurement to decimal feet first.

c. will the couch fit into the available space?

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.