# mathematics

*label*Mathematics

*timer*Asked: Aug 3rd, 2018

*account_balance_wallet*$15

**Question description**

1.The illumination provided by a car’s headlight varies inversely as the square of the distance from the headlight. A car’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 one’s weight, in pounds, and inversely as the square of one’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.One’s intelligence quotient, or IQ, varies directly as a person’s mental age and inversely as that person’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.

## Tutor Answer

hello, here is the complete work. please feel free to let me know if there are edits that you want me to do. thank you.

1. The illumination provided by a car’s headlight varies inversely as the square of the distance

from the headlight. A car’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?

I=k/D2

Whereby

K is a constant

I is the illumination by the headlight

D is the distance from the headlight

If I is 3.75 foot handles and D is 40 then K will be

3.75 =k/402

3.75 = k/1600

3.75 *1600 = k

K...

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