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Solve the initial value problem:
y'=(1+3X^2)/(3y^2-6y), Y(0) =1
And determine the interval in which the solution is valid.
Hint: To find the interval of definition look for points where the intergral curve has a vertical tangent.
0 2 4 1 3 5 (imagine the vertical sets of numbers are surrounded by a large parenthesis, as it is in a binomial expression)
A box is made from a sheet of metal that is 8 meters by 10 meters, by removing a square from each corner of the sheet and folding up the sides. Find the width of the square to removed in order to have a box of maximum volume.
The general manager of a construction company compiled the ages of 50 newly hired unskilled employees. The data is shown, what is the median age.
Let phi : R^2 --> R be a function given by phi(x,y) = x^3 + xy + y^3 +1 For which points p =(0,0) , p=(1/3,1/3), p =(-1/3,-1/3) is the subset phi^-1 ( phi(p)) an imbedded sub-manifold of R^2.
Provide probability distribution, histogram, and find the expected value of a coin that is tossed 3 times
The format for the final answer should be similar to this one: if the problem is tan^(-1) * (2i). answer: (n + 1/2)*pi + (i/2) * ln(3) , (n =0, +-1, +-2,...)
Probability of Having a Disease when Testing Positive. Suppose that 1% of all people have a particular disease. A test for the disease is 99% accurate. This means that a person who tests positive for the disease has a 99% chance of actually having..
Find the rate of change.
Let f : [0,1]-->[0,1] be a continuous function. Show that there exists a real number x in [0,1] such that f(x)=x (apply the intermediate value theorem to the function f(x) -x).
The combined degrees of freedom
Let X be a continuous random variable with the PDF f and the CDF F. Assume that f(x) > 0 for all real numbers x. Define the random variable Y = F (X ). Show that Y is uniform in the interval [0, 1].
Given a rational function, identify a method which can be used to determine if there is a vertical asymptote.
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