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Q1: Find three positive numbers whose sum is 54 and whose product is as large as possible.
Q2: Let f(x,y) = x2 +3y -3xy and R is the triangular region with vertices (0, 0), (2, 0) and (2, 2). Find the interior and boundary points only at which the absolute extrema of f(x, y) can occur.
Write mathematical expression for the given statement and Solve and find the value of unknown.
A simple question on the Mean of a Binomial distribution, 80% of the community favored building a police substation in their neighborhood.
Waiting Lines and Queing Theory Models. Customers enter the waiting line at a cafeteria on a first come, first served basis in two serving lines.
Recall that S_N (f)(x)= sum (n=-N to N) c_n e^{inx}= 1/2pi integral (from -pi to pi) f(x-t)sin ((N+1/2)t)/sin(t/2) dt
Filling a tank. A water tank has an inlet pipe and a drain pipe. A full tank can be emptied in 30 minutes if the drain is opened and an empty tank can be filled in 45 minutes with the inlet pipe opened.
At the [I.CI level of significance, test the claim that the mean eight of women with Turner's syndrome is less than that of the general female population]
Find the slope of the line 2x + y = 4. Find the point of intersection of the lines x + y = 5 and 3x - y = 7. Graph the pair of lines.
What are the co-ordinates of the point of intersection of lines M and N? Write the co-ordinates of the intersections of lines M and N with the x-axis. Write the co-ordinates of the intersection of lines M and N with the y-axis.
Solving problems conditional probability
What would be the scheduling model for this situation (environment, restriction, constraints) if you wish to minimize the total time in system? Use the appropriate scheduling notation.
Find the derivative of f(x)= (3-4x^2)/(x^2-x-6) and then determine intervals of increase/decrease,local max and min values and points of concavity or inflection.
Rate of change over the time intervals .
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