# Questions & Answers

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- A rectangular package to be sent by a postal service that has a maximum total length and perimeter (or girth) limit of 108 inches. A rectangular package is to be sent via this service. Calculate the dimensions of the package that covers the maximum volume. (Cross-sections may be assumed to be square)
- Coffee is draining from a conical filter into a cylindrical coffee pot of radius 4 inches at the rate of 20 cubic inches per minute. How fast is the level in the pot rising when the coffee in the cone is 5 inches deep. How fast is the level in the cone falling then?
- Find the change of coordinates matrix from B to the standard basis in R^n.
- Find the least integer n such that f(x) is O(x^n) for each of these functions.
- Determine the longest interval in which the given initial value problem is certain to have a unique twice differentiable solution. Do not attempt to find the solution.
- Determine whether f is a function from Z to R for given functions
- If the atomic radius of lead is 0.175 nm, calculate the volume of its unit cell in cubic meters.
- A standard deck of cards contains 52 cards. One card is selected from the deck.
- A boat is pulled into a dock by means of a winch 12 feet above the deck of the boat.
- Find two functions f and g such that (f ∘ g)(x) = h(x).
- Suppose that X is a normal random variable with mean 5. If P(X>9)=0.2, approximately what is Var(X)?
- If X is an exponential random variable parameter, λ = 1 , compute the probability density function of the random variable Y defined by Y = logX.