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A farmer has 200 yards of fencing with which to enclose a rectangular field. One side of the field can make use of a fence that already exists. What is the maximum area that can be enclosed?
At the end of the year, the total interest from these investments was $940. How much was invested at each rate?
Let V be an n-dimensional vector space over F. What is the characteristic polynomial of the Identity operator on V? What is the characteristic polynomial for the zero operator?
How do you explain why vectors QR and RQ are not equivalent? Explain when the elimination method for solving a system of equations is preferable to the substitution method.
Sketch all the nonisomorphic, simple graphs that have 5 vertices and 5 edges.
Find the indicated probability.
The half-life of cesium-137 is 30 years. Suppose we have a 170 mg sample.
The speed of a passenger train is 18 mph fasster than the speed of a freight train. The passenger train travels 280 miles in the same time it takes the freight train to travel 190 miles. Find the speed of each train.
Find the volume of a frustum of a pyramid with square base of side 30, square top of side 15 and height 10.
A rectangular storage unit has dimensions 1 m by 2 m by 3 m. If each linear dimension is increased by the same amount. What increase would create a new storage unit with a volume 10 times the original
The problem asks me to sketch the curve represented by the vector-valued function. The vector-valued function is:
Consider the curve 5x3+8xy+5y2 = 45. Use implicit differentiation to calculate the derivative dy/dx. Hence determine the point/s which has/have a horizontal tangent.
Permutation and combination
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