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Problem 1. Find the maximum and the minimum distance from the origin to the ellipse x 2 + xy + y 2 = 3. Hints: (i) Use x 2 + y 2 as your objective function; (ii) You c
how to find value of cos20 without using calculator
Demonstrates that f ( x ) = 4 x 5 + x 3 + 7 x - 2 has accurately one real root. Solution From basic Algebra principles we know that since f (x) is a 5 th degree polynomi
The Limit : In the earlier section we looked at some problems & in both problems we had a function (slope in the tangent problem case & average rate of change in the rate of chan
Now we have to discuss the basic operations for complex numbers. We'll begin with addition & subtraction. The simplest way to think of adding and/or subtracting complex numbers is
Find out the x-y coordinates of the points in which the following parametric equations will have horizontal or vertical tangents. x = t 3 - 3t y = 3t 2 - 9 Solut
Identify the surface for each of the subsequent equations. (a) r = 5 (b) r 2 + z 2 = 100 (c) z = r Solution (a) In two dimensions we are familiar with that this
Marc goes to the store with exactly $1 in change. He has at least one of each coin less than a half-dollar coin, but he does not have a half-dollar coin. a. What is the least nu
Does the Angle-Side Relationship Theorm work for all triangles or just a certain type of triangle? Does is correspond with the orthocenter of a triangle?
what is a liter
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