Homework Questions
Section 6.7 Variation Problems
Suppose I pay you $10 per hour to do a job.
Y varies directly as x.
When y = 80 we know x = 5.
Find the value of y when x = 11.
6.7 Steps to solve variation problems of any sort:
Handout
1. Write a general model using variables that describe the quantities. Be sure to include k.
2. From the problem, fill in the variables you are given and solve for k.
3. Write a specific model for your situation using the variables and the value for k.
4. Use the model to answer any additional questions.
Example
y varies directly as the square of x. x = 2 when y = 6. Find x when y = 7.5
Example
The speed of an auto in miles per hour (mph) varies directly with the speed in kilometers per hour (kmh). A speed of 64 mph is equivalent to a speed of 103 kmh. You are driving through Canada at 55 mph. How fast is this in kmh?
Example
The distance a body falls varies directly as the square of the time of the fall. A skydiver falls 64 feet in 2 seconds.
How far will he fall in 3.5 seconds? Other kinds of variation too.
Inverse Variation
y varies inversely as x. y = 10 when x = 2.
Find y when x is 5.
Joint Variation
Y varies directly as x and z.
When y = 16 we know x = 2 and z = 4.
Find y when x = 3 and z = 10.
Example Boyle's Law states that under certain conditions, the pressure of a gas varies inversely with its volume. A sample of hydrogen gas has a volume of 8.56 liters at a pressure of 1.5 atmospheres. Find the volume of the hydrogen gas if the pressure is 1.2 atmospheres.