1. Find the variation constant and an equation of variation where y varies directly as x, and y = 4 when x=39.
2. Find the variation constant and an equation of variation where y varies inversely as x, and y = 15 when x = 15.
3. [Hook's Law] The distance d, when a spring is stretched by a hanging object, varies directly as the weight w of the object. If the distance is 30 cm when the weight is 2 kg, what is the distance when the weight is 7 kg?
4. The number of kilograms of water in a human body varies directly as the mass of the body. A 96-kg person contains 64 kg of water. How many kilograms of water is in a 72-kg person?
5. [Electrical current] The current I in an electrical conductor varies inversely as the resistance R of the conductor. The current is one-fifth Ampere when the resistance is 3750 ohms. What is the current when the resistance is 1350 ohms?
6. The intensity I of light from a light bulb varies inversely as the square of the distance d from the light bulb. Suppose I is 1000 w/m^2 when the distance is 7 m. How much farther would it be to a point where the intensity is 810 w/m^2 ?
This solution is comprised of detailed step-by-step calculations and analysis of the given ratio and proportion problems. It also provides a clear perspective of the underlying concepts.