On a camping trip, you decide to hang your backpack from a rope stretched between two trees, so bears can’t steal your food while you sleep. The trees are 20 feet apart, and the rope is tied to each tree at a spot 12 feet above the ground. When you hang your backpack on the rope, the weight of the pack pulls the rope down a little—each side of the rope now makes an angle of 15 degrees with the horizontal. That night, a bear comes into your camp and tries to get your backpack with the food in it. Standing on its back legs, the bear can reach 8 feet into the air. Is your stuff safe? (Your backpack is two feet long.)

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