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Question: Of all rectangles with given area, A, which has the shortest diagonals?
A rectangular beam is cut from a cylindrical log of radius 30 cm. The strength of a beam of width w and height h is proportional to wh2. (See Figure) Find the width and height of the beam of maximum strength.
(a) Give examples of sequences {an}, {bn} which both diverge, yet {anbn} converges. (b) Give examples of sequences {an}, {bn} which both diverge, yet {an + bn} converges.
There are three different roads from Cupids to Harbour Grace and five different roads from Harbour Grace to Heart's Desire.
What is the largest domain over which this function is defined? For this domain, what is the corresponding range of the function?
Show that ℘ is real-valued on all these lines, and hence on the boundaries of all these rectangles.- Prove that ℘ maps the interior of each rectangle conformally to the upper (or lower) half-plane.
Show that the relation of logical equivalence on the set of all compound propositions is an equivalence relation. What are the equivalence classes of F and of T?
Prove that (3p+1)^4-1,where p is prime greater than 3,has at least 4 prime distinct factors.
Suppose that ydx + (yx^2-x)dy = 0 has an integrating factor that is a function of x alone [i.i., mu = mu(x)]. Find the integrating factor and use it to solve the differential equation.
Use the extended Euclidean algorithm to find the greatest common divisor of the given numbers and express it as a linear combination of the two numbers.
How much did it cost, per person screened, for the initial cholesterol testing? Remember that each provider on site incurs costs to travel form the health department to the site and back.
Describe specifically how you will use the technology to create the computer-based simulation model.
question a company has three new machines of different types. there are four different plants that could receive the
what proportion of the families spends $85 or more per week on food?
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