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Prove each of the following identities.
The base of an aquarium with volume V = 330 is made of slate and the sides are made of glass. If slate costs five times as much (per unit area) as glass, find the dimensions of the aquarium that minimize the cost of the materials.
A 30 in piece of string is cut into two pieces. One piece is used to form a circle and the other to form a square. How should the string be cut so that the sum of the areas is a minimum?
Consider the following three vectors in R^3: Verify that {x_1, x_2, x_3} are orthogonal with the standard inner product in R^4
What is the expected point value of a random guess? Is it advantageous to guess under these circumstances?
car a is travelling north at 90 kmh and car b is travelling west at 80 kmh both approaching the intersection of their
Suppose that each member of a set of people has a list of k books which he or she wishes to borrow from a library. SUppose also that each book appears on exactly k lists. Show that it is possible for everyone to borrow one of the books on his or h..
The length of the shadow of a 200 foot tower is 70 feet. find the angle of elevation of the sun.
Two cables are pulling on a steel beam. Both attached at the same location (0, 0). the first cable pulls with a force of 1 500 newtons at a 76° angle and the second cable pulls with a force of 2100 newtons at a 138° angle.
For a class of 43 students, for a certain exam, the mean grade is 67 and the standard deviation is 7, how many students should receive a C?
solve the given equation and solve the equation by factoring.solve the equation using the method of your choice 3xx - 3
List and discuss the different properties, which will classify the group as a dihedral group of order 8.
What is the percentage of people reading none of the newspapers
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