Combined Variation

Write the mathematical equation of the given statement: (no spacing, use / for fraction bar)

f is directly proportional to b and inversely proportional to e

(a)  

Write the mathematical equation of the given statement: (no spacing, use / for fraction bar)

The time (t) needed to answer a set of problems is directly proportional to the number (N) of problems, and inversely proportional to the number of students (P) working on the solutions.

(a)  

Solve for the constant of variation, k.

A varies directly as D and inversely as F. A=10.5, when D=2 and F=4

(a)  

Solve for the constant of variation, k.

D is directly proportional to e² and inversely proportional to f. D=12, when e=2 and f=7.

(a)  

Given that z varies directly with y and inversely with x when x = 12, y=36 and z=15, find the value of z when x= -8 and y=24.

(a)  

If a varies jointly as b and c, and inversely as d when a=140, b=5, c=4, and d=3, find a when b=10, c=8, and d=12.

(a)  

The volume of gas varies directly as the temperature and inversely as the pressure. If the volume is 180 cu cm when the temperature is 270 K and the pressure is 15 lbs/sq cm, what is the volume when the temperature is 220 K and the pressure is 25 lbs/sq cm? (Write your final answer in this form: _ cu cm )

(a)  

The resistance of a wire varies directly as its length and inversely as the square of the diameter. If a 15-ft long wire and a diameter of 1/2 inch has a resistance of 3 ohms, what is the resistance of a wire with a length of 25 ft and a diameter of 2 inches? (Write your final answer in fraction and of the form: _ ohms )

(a)