Your neighborhood movie theater has a 25-foot-high screen located 8 feet above your eye level. If you sit too close to the screen, your viewing angle is too small, resulting in a distorted picture. By contrast if you sit too far back, the image is quite small, diminishing the movie's visual impact. If you sit LaTeX: xx feet back from the screen, your viewing angle is given by LaTeX: \theta = \tan^{-1} \frac{33}{x} - \tan^{-1} \frac{8}{x} θ = tan − 1 ⁡ 33 x − tan − 1 ⁡ 8 x 1) Choose a value for LaTeX: xx representing how far back you want to sit in feet and use the formula above to calculate the viewing angle LaTeX: \thetaθ for that distance. Make sure your calculator is in radian mode. 2) Go to Movie Theater Viewing Angle and compare your choice of distance to the optimal choice of distance. How close or far are you to the optimal (maximum) viewing angle? 3) What is your viewing angle θ in degrees? (convert your angle to the nearest tenth)

Asystem of linear equations with more equations than unknowns is sometimes called an overdetermined system. can such a system be consistent? illustrate your answer with a specific system of three equations in two unknowns. choose the correct answer below. a. yes, overdetermined systems can be consistent. for example, the system of equations below is consistent because it has the solution nothing. (type an ordered pair.) x 1 equals 2 comma x 2 equals 4 comma x 1 plus x 2 equals 6 b. no, overdetermined systems cannot be consistent because there are fewer free variables than equations. for example, the system of equations below has no solution. x 1 equals 2 comma x 2 equals 4 comma x 1 plus x 2 equals 12 c. yes, overdetermined systems can be consistent. for example, the system of equations below is consistent because it has the solution nothing. (type an ordered pair.) x 1 equals 2 comma x 2 equals 4 comma x 1 plus x 2 equals 8 d. no, overdetermined systems cannot be consistent because there are no free variables. for example, the system of equations below has no solution. x 1 equals 2 comma x 2 equals 4 comma x 1 plus x 2 equals 24