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Prove carefully: " a, b, c, d Î R, if a < b and c > d, then ad + bc > ac + bd.
HINTS: What can you deduce about the sign of (b - a)(d - c), and what do you get when you multiply this out?
You can assume that the usual algebraic rules of inequalities apply, without citing an axiom or theorem.
How can equations and inequalities help a business maximize cost and minimize costs ? What is the importance of understanding how to set up and solve equations and inequalities ? Discuss in general without a mathematical example.
A grain silo has a cylindrical shape. Its diameter is 19 , and its height is 38 . What is the volume of grain that can be stored in the silo?
consider de quadratic function yaxsup2bxca. use the mathematical and graphical analyses to deterine the equation of the
Rita has a collection of 108 coins consisting of nickels, dimes, and quarters. The number of dimes is 4 more than one-third the number of nickels, and the number of quarters is twice the number of dimes. How many coins of each kind does she have?
Why must we always be mindful of the final value of the denominator in a rational expression? For example, consider the rational expression 3x/(x2 - 16). What values in the denominator must we be mindful of? Explain why.
integral over gamma of e^(iz) / z^2 dz, where gamma(t) = e^(it), 0=
1discuss how atkins method can improve the convergence of a numerical scheme2discuss the pros and cons for netwons
Water leaks from a vertical cylindrical tank through a small hole in its base at a rate proportional to the square root of the volume of water remaining. The tank initially contains 250 liters and 23 liters leak out during the first day. When will..
Find parametric equations for the tangent line to the curve given by parametric equations x = 1 + 2√t, y = t3 - t, z = t3 + t, at the point (3, 0, 2)
one cell phone company charges 0.10 per minute with no activation fee. another cell phone service charges 0.05 per
The following arguments are deductive.- Since Winston Churchill was English, and Winston Churchill was a famous statesman, we may conclude that at least one Englishman was a famous statesman.
Define a relation L on R x R (i.e the Euclidean plane with the usual Cartesian coordinates) by the rule (x, y) L (z, w) if and only if x - y = z - w. Show that L is an equivalence relation. Then describe the equivalence classes.
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