# Questions & Answers

### 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)

This question aims to learn the basic methodology for optimizing a mathematical function (maximizing or minimizing). Critical points are the points

### 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?

The aim of this question is to use the geometric formulas of volume of different shapes for the solution of word problems. The volume of the

### Find the change of coordinates matrix from B to the standard basis in R^n.

, Bigg , Bigg right} } ] The aim of this question is to find the change-of-coordinates matrix given

### Find the least integer n such that f(x) is O(x^n) for each of these functions.

$f(x)=2x^{2}+x^{3}log x$ $f(x)=3x^{5}+(log x)^{4}$ $f(x)=dfrac{x^{4}+x^{2}+1}{x^{4}+1}$ The article aims to find the value of the n for each

### 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.

( x + 3 ) y”  +  x y’  +  ( ln|x| ) y  =  0,  y(1) =  0,  y'(1)  =  1  The aim of this question is to

### Determine whether f is a function from Z to R for given functions

$f(n) =pm n$ $f(n) = sqrt {n^2 + 1}$ $f(n) = dfrac{1}{n^2 -4}$ The aim of this question is to find out if the given equations are functions from

### If the atomic radius of lead is 0.175 nm, calculate the volume of its unit cell in cubic meters.

The aim of this question is to calculate the volume of a unit cell, giving due attention to the lettuce structure of the given metal. The uniform

### A standard deck of cards contains 52 cards. One card is selected from the deck.

Compute the probability of randomly selecting a spade or diamond. P(spade or diamond) Compute the probability of randomly selecting a spade or

### A boat is pulled into a dock by means of a winch 12 feet above the deck of the boat.

The rope is pulled by a winch at 4 feet per second. When 14 feet of rope is out, what will be the speed of the boat? As the boat inches closer to the

### Find two functions f and g such that (f ∘ g)(x) = h(x).

The question aims to find the functions f and g from a third function which is a composition of the function of those two functions. The composition

### Suppose that X is a normal random variable with mean 5. If P(X>9)=0.2, approximately what is Var(X)?

JUMP TO TOPICExpert AnswerExample 1SolutionExample 2SolutionExample 3Solution This question aims to find the probability of a normally distributed

### If X is an exponential random variable parameter, λ = 1 , compute the probability density function of the random variable Y defined by Y = logX.

This problem aims to familiarize us with the probability density functions. The concepts required to solve this problem are continuous random