Name
MATH 105 PRACTICE MIDTERM II Please work out each of the given
problems. Credit will be based on
the steps that you show towards the final answer.
Show your work. PROBLEM 1 (7 Points each) Please answer the following true or false. If false, explain why or provide a counter example. If true, explain why.
PROBLEM 2 Consider the function (22 Points) _{ } Without the use of the graphing capabilities of your graphing calculator, for the following two functions
PROBLEM 3 (20 Points) As you are standing outside on a beautiful sunny late afternoon, you notice that your shadow is growing in length at a rate of 2 feet per hour. If you are 6 feet tall, how fast is the angle of elevation of the sun decreasing when your shadow is 8 feet long? PROBLEM 4 (20 Points Each)
PROBLEM 5 (20 Points) Sketch the graph of a function
with the following properties:
PROBLEM 6 (20 Points) You plan to build a rectangular office building of minimal cost with a with a wall down the middle to subdivide the building into two offices as shown in the picture. The outer walls cost $500 per foot to construct and the divider wall costs $100 per foot to construct. If the combined square footage of the two offices is to be 1,000 square feet, what dimensions should you make the building?
