Lesson 7

Lesson 7: Modelling Problems with Radical Equations

 

Focus

 

The length of one year on a planet is equal to the time it takes that planet to complete one orbit of its star. It takes Earth 365 days to orbit its nearest star, the Sun. It only takes the planet Mercury 87.96 Earth days to complete one orbit of the Sun, so a year on Mercury is much shorter than a year on Earth. The planet Jupiter takes 11.83 Earth years to complete its orbit of the Sun, so a year on Jupiter is much longer than a year on Earth.

 

The relationship between a planet’s orbit and its distance from the Sun was discovered by Johannes Kepler in 1619. He proved that the farther a planet is from the Sun, the longer it takes to complete one orbit (called the period). This relationship, known as Kepler’s third law, states that the square of the orbital period is proportional to the cube of the distance the planet is from the Sun and is represented by the following equation:

 

T2 = Kr3

 

If you isolate the period, T, you get where T is the orbital period (the time it takes to make a single orbit), K is a proportionality constant, and r is the maximum distance from its star.

 

As you have seen throughout this module, radical expressions are used to solve problems in many situations. In this lesson you will use radical equations to model different situations in order to solve problems. You will see that radical equations can not only be used to find the length of a year on different planets but also to find the dimensions of a soccer field, the amount of current in a hair dryer, or how to find the dimensions of a TV screen. These are, of course, only a few examples of the use of radicals.

 

This lesson will help you answer the following inquiry question:

• How do you use radical equations to model situations when solving problems?

Assessment

• Lesson 7 Assignment

All assessment items you encounter need to be placed in your course folder.

 

Save a copy of the Lesson 7 Assignment to your course folder. You will receive more information about how to complete the assignment later in this lesson.

Materials and Equipment

• calculator