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Sigma notation expansion, How do you expand a sigma notation from x to x of...

How do you expand a sigma notation from x to x of a variable that is not defined in the index. For example, summation of i=1 to n of x?

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Write the equation of the circle in standard form. Find the center, radius, intercepts, and graph the circle. ??2+??2+16??-18??+145=25.

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In his boat, Leonard can travel 24 miles upstreamin the same time it takes to travel 36 miles downstream

Using linear algebra calculate the equilibrium , using linear algebra calcu...

using linear algebra calculate the equilibrium P 1 ,P 2 ,P 3 for the following three good market model. (1) Qs1=-7+P1 (2) Qd1=15-P1+2P2+P3 (3) Qs1=Qd1 (4) Qs2=-4+4P2

Example of rational inequalities, Solve (3x+ 1/ x + 4 ) ≥ 1. Solution ...

Solve (3x+ 1/ x + 4 ) ≥ 1. Solution The first thing that we have to do here is subtract 1 from both of sides and then get everything in a single rational expression.  (3

Lagrange multipliers, 1. In real world optimisation problems there is often...

1. In real world optimisation problems there is often an accompanying constraint that must also be satisfied. These problems are typically solved using "Lagrange Multipliers", whic

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