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Chapter 1: Problem 4
Determine whether the equation is linear in the variables \(x\) and \(y\). $$x^{2}+y^{2}=4$$
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Solve the system using either Gaussian elimination with back-substitution or Gauss-Jordan elimination. $$\begin{array}{ll} 2 x_{1}+\quad\quad\quad\ 3 x_{3}=&3 \\ 4 x_{1}-3 x_{2}+7 x_{3}= & 5 \\ 8 x_{1}-9 x_{2}+15 x_{3}= & 10 \end{array}$$
Solve the system using either Gaussian elimination with back-substitution or Gauss-Jordan elimination. $$\begin{aligned} x_{1}+x_{2}-5 x_{3} =3 \\ x_{1} -2 x_{3}=1 \\ 2 x_{1}-x_{2}-x_{3} =0 \end{aligned}$$
(a) determine the polynomial function whose graph passes through the given points, and (b) sketch the graph of the polynomial function, showing the given points. $$(-1,3),(0,0),(1,1),(4,58)$$
In the 2007 Fiesta Bowl Championship Series on January 8 \(2007,\) the University of Florida Gators defeated the Ohio State University Buckeyes by a score of 41 to \(14 .\) The total points scored came from a combination of touchdowns, extra-point kicks, and field goals, worth \(6,1,\) and 3 points, respectively. The numbers of touchdowns and extra-point kicks were equal. The number of touchdowns was one more than three times the number of field goals. Write a system of equations to represent this event. Then determine the number of each type of scoring play. (Source: www.fiestabowl.org)
Use \(\log _{2} 1=0, \log _{2} 2=1,\) and \(\log _{2} 4=2\) to estimate \(\log _{2} 3\)
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