Problem 1 [[3 points). Consider the equation x4 7er + [3x 10 = 0 on the interval [2. 3]. {a} Explain why we know that there is a root in the given interval. (Hint: Think back to the Bisection Method.) {b} Use Newton's Method to approximate the root accurate to four decimal places. Problem 2 {4 points}. [This is Question [3 on lQuiz 8.) A gigantic hour glass in the shape of a cone is leaking sand at a constant rate of 2m3/hour. The base radius of the hour glass is 4111 and the height is 8111. At what rate is the height of the sand in the hour glass changing when the depth of the sand is 3m? Hint: Relate the volume of the sand with the radius and the height and use implicit differ entiation. Then use similar triangles to relate the radius and height of the sand and replace the rate at which the radius is changing in the equation found in the previous step. Problem 3 [10 points}. At horse barns. horses are often separated by dietary requirements and age. A local barn wants to separate their horses into four groups {strict diet. light diet. regular. and seniors}. They got 750m of fencing panels on sale and will use these to set up the four pens. which should be rectangular and sharing sides [one big rectangular area divided into four equal smaller areas. as shown in the diagam below). Which dimensions should they use to maximize the total fenced in area and what is this maximum area