1.The illumination provided by a carâ€™s headlight varies inversely as the square of the distance from the headlight. A carâ€™s headlight produces an illumination of 3.75 foot-candles at a distance of 40 feet. What is the illumination when the distance is 50 feet?
2.Body-mass index, or BMI, takes both weight and height into account when assessing whether an individual is underweight or overweight. BMI varies directly as oneâ€™s weight, in pounds, and inversely as the square of oneâ€™s height, in inches. In adults, normal values for the BMI are between 20 and 25, inclusive. Values below 20 indicate that an individual is underweight and values above 30 indicate that an individual is obese. A person who weighs 180 pounds and is 5 feet, or 60 inches, tall has a BMI of 35.15. What is the BMI, to the nearest tenth, for a 170-pound person who is 5 feet 10 inches tall? Is this person overweight?
3.Oneâ€™s intelligence quotient, or IQ, varies directly as a personâ€™s mental age and inversely as that personâ€™s chronological age. A person with a mental age of 25 and a chronological age of 20 has an IQ of 125. What is the chronological age of a person with a mental age of 40 and an IQ of 80?
4.Kinetic energy varies jointly as the mass and the square of the velocity. A mass of 8 grams and velocity of 3 centimeters per second has a kinetic energy of 36 ergs. Find the kinetic energy for a mass of 4 grams and velocity of 6 centimeters per second.