Learning Objectives In this section, you will: Figure 1 Planets orbiting the sun follow elliptical paths. (credit: NASA Blueshift, Flickr) Most of us are familiar with orbital motion, such as the motion of a planet around the sun or an electron around…
Learning Objectives In this section, you will: As we have seen, conic sections are formed when a plane intersects two right circular cones aligned tip to tip and extending infinitely far in opposite directions, which we also call a cone. The…
Learning Objectives In this section, you will: Figure 1 Katherine Johnson’s pioneering mathematical work in the area of parabolic and other orbital calculations played a significant role in the development of U.S space flight. (credit: NASA) Katherine Johnson is the pioneering NASA mathematician…
Learning Objectives In this section, you will: What do paths of comets, supersonic booms, ancient Grecian pillars, and natural draft cooling towers have in common? They can all be modeled by the same type of conic. For instance, when something moves…
Learning Objectives In this section, you will: Figure 1 The National Statuary Hall in Washington, D.C. (credit: Greg Palmer, Flickr) Can you imagine standing at one end of a large room and still being able to hear a whisper from a person…
The rings of Saturn have produced wonder, as well as misunderstanding, since Galileo first discovered them (he initially thought they were moons). Though they appear to be a series of solid discs even in this 2004 closeup from the Cassini…
Systems of Linear Equations: Two Variables Systems of Linear Equations: Three Variables Systems of Nonlinear Equations and Inequalities: Two Variables Partial Fractions Matrices and Matrix Operations Solving Systems with Gaussian Elimination Solving Systems with Inverses Solving Systems with Cramer’s Rule
Learning Objectives In this section, you will: We have learned how to solve systems of equations in two variables and three variables, and by multiple methods: substitution, addition, Gaussian elimination, using the inverse of a matrix, and graphing. Some of…
Learning Objectives In this section, you will: Soriya plans to invest $10,500 into two different bonds to spread out her risk. The first bond has an annual return of 10%, and the second bond has an annual return of 6%.…
Learning Objectives In this section, you will: Figure 1 German mathematician Carl Friedrich Gauss (1777–1855). Carl Friedrich Gauss lived during the late 18th century and early 19th century, but he is still considered one of the most prolific mathematicians in history. His contributions to…