Algebra 51 - Three Variable Systems in the Real World - Problem 3

Professor Von Schmohawk explains how to use a system of three linear equations to solve a problem on Coco Loco Island, where a monument must be placed in a circular amphitheater touching three sacred palm trees. The lecture covers the mathematical process of determining the circle's center and radius using linear equations, and concludes with a preview of future topics on matrices.

What type of shapes can systems of linear equations help calculate?

• Only linear shapes

• Nonlinear shapes like parabolic trajectories

• Only triangular shapes

• Only circular shapes

What was the King's decree regarding the meeting of Coco Loconians and Bongoponganians?

• To build a new palace

• To write a new history book

• To declare a national holiday and erect a monument

• To start a new festival

How did the mathematician propose to solve the problem of the circle?

• By using a computer program

• By guessing the center and radius

• By using a system of three linear equations

• By using a compass and ruler

What are the coordinates of the sacred palm trees?

• (7, 3), (9, 5), (11, 8)

• (8, 1), (11, 4), (12, 10)

• (6, 2), (10, 4), (12, 9)

• (9, 2), (10, 3), (10, 9)

What is the first step in solving the system of equations for the circle?

• Measuring the distance between the palms

• Drawing the circle on a graph

• Writing the equations in standard form

• Guessing the values of C, D, and E

What is the value of D after solving the equations?

• 12

• -12

• 24

• -24

What is the radius of the circle that touches all three sacred palms?

• 5 units

• 7 units

• 4 units

• 6 units

What did the mathematician become after solving the problem?

• A celebrity on Coco Loco island

• A royal advisor

• The king's personal mathematician

• A teacher at Why U

What is the future topic mentioned that will help solve systems of equations?

• Using graphs

• Using matrices

• Using calculus

• Using trigonometry

What is the advantage of using matrices in solving systems of equations?

• They require less data

• They simplify calculations regardless of the number of variables

• They are easier to draw

• They are more accurate