I'm at my wits end with my Calculus homework. I have a test tomorrow and I must have an 80% on every assignment or I will be unable to take the test. I'm done with a lot of it but at this point my brain is mush and I hit a brick wall with every problem or am unable to even set up the problems to begin with.
1. Find two positive numbers whose product is 218 and whose sum is a minimum. (Give your answer correct to 2 decimal places.)
___ (smaller number)
___ (larger number)
2. Consider the function below.
Find the point on the graph of function that is closest to the point (-3, 12).
3. On a given day, the flow rate F (in cars per hour) on a congested roadway is given by the equation below, where v is the speed of traffic in miles per hour.
What speed will maximize the flow rate on the road? (Give your answer correct to 1 decimal place.)
4. Determine the dimensions of a rectangular solid (with a square base) with maximum volume if its surface area is 343.5 square centimeters. (Give your answer correct to 2 decimal places.)
___ cm (length)
___ cm (width)
___ cm (height)
5. An offshore oil rig well is 1 kilometers off the coast. The refinery is 5 kilometers down the coast. Laying pipe in the ocean is twice as expensive as on land. What path should the pipe follow in order to minimize the cost? Complete the following statement. (Give your answer correct to 2 decimal places.)
The pipe should be laid in the ocean from the rig to a point on the coast ______ km from the refinery, then on land the remainder of the distance to the refinery.
Any help would be appreciated.