Superlesson
Project 5-3
Advanced Algebra
Chapter 5, Quadratic Functions and Relations
Mathematics is central to the study of health and medicine. In their investigations, medical researchers often encounter conic sections, sometimes in unexpected places.
Part A, Circles
1. Look at an image of a cauliflower Mosaic virus.
a. The image you see is a portion of an electron microscope scan of a photograph measuring approximately 24 cm by 19 cm. By scanning left-right and up-down, estimate the actual dimensions of a photo section that appears in your viewing screen.
b. Measure the radius of a typical virus on your screen. Then estimate the radius of a virus as it appears in the photo.
c. Write the radius of the virus, as it appears in the photo, in nanometers (1 cm = 107 nm).
d. Use the magnification of the electron microscope image to approximate the actual radius of the virus in nanometers.
e. If you graphed the virus on an xy-coordinate axis with the virus's center at the origin, what would its equation be? (1 unit = 1 nm)
Part B, Ellipses
2. Look at the image of the lithotripter beside the section "What Are the Advantages of Lithotripsy?"
a. Sketch the lithotripter, the kidney stone, and the shock waves as shown in the photo.
b. On your sketch, draw the major axis of the ellipse off which the shock waves bounce. Identify the vertices, foci, and center.
c. The distance from the vertex to the focus is 2 cm. The distance from the focus to the center is 8 cm. Write the equation of the ellipse.
Part D, Hyperbolas/Making Connections
3. Estimate the speed and distance traveled of a deadly virus.
a. Find how long it took the 1918-1919 Influenza virus to spread from the coast of Europe, where it arrived on American troop ships, to Poland, a distance of approximately 1200 km.
b. Approximate the speed at which the virus traveled, in miles per day.
c. Public health officials in Allain detected the virus on May 5. Officials in Belnais, 200 km away, detected it on May 13.
How much farther from the point where the virus first struck Europe was Belnais than was Allain? (Call this distance d.)d. Draw the line segment shown above. Draw a point on the segment whose distance from Belnais exceeds its distance from Allain by d km. How far is the point from Allain?
e. Estimate the position and draw at least 6 other points whose distance from Belnais exceeds its distance from Allain by d km.
f. What conic section have you drawn a portion of? How do you know?
g. How could health officials find where the virus struck Europe?
