Download Unit 13 – Classwork 4

Unit 16 – Classwork 4
Thursday, May 19
The word problems on this worksheet were taken directly from Paul Foerster’s
Algebra and Trigonometry textbook, copyright 1999, Addison-Wesley Publishing
1. In the graph below, y varies __________________ with the square of x.
If the graph contains the point (20, 0.355), find the particular equation
expressing y in terms of x.
2. In the graph below, y varies __________________ with the square root
of x. If the graph contains the point (16, 10.4), find the particular
equation expressing y in terms of x.
3. In 1844 the French scientist J.L. Poiseuille found that the rate at which a
fluid such as blood flows through small tubes such as arteries and veins
varies directly with the product of the pressure acting on the fluid and the
fourth power of the radius of the tube. Assume that you have an artery
0.2 centimeters in radius through which blood flows at 400 cubic
centimeters per second when acted upon by the normal pressure of 100
units.
a. Write the particular equation expressing flow rate in terms of
pressure and radius.
b. If the radius of the artery were reduced to 0.16 cm due to the build
up of cholesterol, what flow rate would be produced by the normal
blood pressure of 100 units.
c. If the heart pumped hard enough to restore the flow rate of 400
cubic millimeters per second for the 0.16 cm artery, what would
the blood pressure be?
4. The weights of airplanes of similar shape are directly proportional to the
cube of their lengths. In order for the airplane to fly, this weight must be
directly proportional to the product of the wing area and the flight speed.
The wing area varies directly as the square of the length of the airplane.
a. Write the general equations from each of the three variation
functions above.
b. From these equations, derive another equation expressing the
speed of the airplane in terms of its length.