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Big Ideas Math Algebra 1, 2015

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Big Ideas Math Algebra 1, 2015 View details

Quiz

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Exercise 16 Page 558

To find the point of intersection, push 2nd and CALC and choose the fifth option, intersect. Then, choose the first and second curve, and pick a best guess for the point of intersection.

Graph:

Volume: About 65450 m^3

Practice makes perfect

We have been given a function that shows the radius r of a sphere which depends on its volume. r=sqrt(3/4πV) We want to find the volume of Spaceship Earth when its radius is 25 meters. To do so, we will use a graphing calculator to graph the given function and r=25 at the same time. Then, we will find the point of intersection by using the intersect feature. Let's first slightly modify our functions by replacing r with y and V with x.

r=sqrt(3/4π V) ⇔ y=sqrt(3/4π x) [0.75em] r=25 ⇔ y=25 To draw the graphs, we press the Y= button and type the functions in two of the rows. Having written the functions, we can push GRAPH to draw. However, we will first change the viewing window settings so that we can see the intersection point.

Notice that the x- and y-values are indicated as non-negative because the radius and the volume cannot be negative. Now, to find the point of intersection, push 2nd and CALC and choose the fifth option, intersect. Then, choose the first and second curve, and pick a best guess for the point of intersection.

The volume of Spaceship Earth is about 65450 cubic meters.

Subchapter links

Exercises p.558