Chapter 13: Problem 35
Find three positive numbers \(x, y\), and \(z\) that satisfy the given conditions. The sum is 30 and the sum of the squares is a minimum.
Chapter 13: Problem 35
Find three positive numbers \(x, y\), and \(z\) that satisfy the given conditions. The sum is 30 and the sum of the squares is a minimum.
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Get started for freeSketch the region of integration and evaluate the double integral. $$ \int_{0}^{1} \int_{0}^{\sqrt{1-x^{2}}} y d y d x $$
Use a double integral to find the area of the region bounded by the graphs of the equations. $$ y=x, y=2 x, x=2 $$
After a change in marketing, the weekly profit of the firm in Exercise 35 is given by \(P=200 x_{1}+580 x_{2}-x_{1}^{2}-5 x_{2}^{2}-2 x_{1} x_{2}-7500\) Estimate the average weekly profit if \(x_{1}\) varies between 55 and 65 units and \(x_{2}\) varies between 50 and 60 units.
Use the regression capabilities of a graphing utility or a spreadsheet to find linear and quadratic models for the data. State which model best fits the data. $$ (0,769),(1,677),(2,601),(3,543),(4,489),(5,411) $$
Sketch the region of integration and evaluate the double integral. $$ \int_{0}^{6} \int_{y / 2}^{3}(x+y) d x d y $$
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