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A poster is to have an area of 180 in2 with 2 inch margins at the bottom and sides and a 7 inch margin at the top. What dimensions will give the largest printed area?
Formulate the above as linear programming problem. Solve (a) by graphical method. Solve using simplex method.
Linear Mappings, Differentiation and Linear Spaces, If l is a nonzero scalar linear function on linear space X (which may be finite or infinite) and a is an arbitrary scalar, there exists a vector x in X st l(x)=a
Find the altitude of a parallelepiped determined by vectors A, B, and C if the base is taken to be the parallelogram determined by A and B and
Check that N(t) = t/(1 +ct) is a solution of the differential equation dN/dt = N^2/t^2. Treat c as an unspecified constant.
Let V be the space of all functions from R to R. It was stated in the discussion session that this is a vector space over R. Prove axioms (VS1)=For all x,y, x+y=y+x (commutativity of addition),
Let S be the circle in the plane {(x,y) in R^2: x^2 + y^2 = 1} and f: S --> R be a continuous map. Show that there exists (x,y) on S such that f(x,y) = f(-x,-y).
Assuming that the total cost per day, C(x), is linearly related to the total output per day, x, write an equation for the cost function.
The sampling distributions of a sample statistic
Use mathematical induction to prove that 2-2*7+2*7^2-.....+2(-7)^n=(1-(-7)^n+1)/4 whenever n is a nonnegative integer. Show that 1^3+2^2+....n^3=[n(n+1)/2]^2 whenever n is a positive integer.
Describe objects that have each of the following types of symmetry.
Suppose the current exchange rate for the Polish zloty is Z 2.85. The expected exchange rate in three years is Z 2.93. What is the difference in the annual inflation rates for the United States and Poland over this period?
Probability: Working with the standard distribution curve. A company installs 5000 light bulbs, each with an average life of 500 hours and a standard deviation of 100 hours, and a distribution approximated by a normal curve
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