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Suppose the maximum healthy weight for a person who is 5 feet 3 inches tall is 170 pounds, and the maximum healthy weight for someone 6 feet 1 inches tall is 220 pounds. The relationship between weight and height here is linear.

(a) Find a linear equation that gives the maximum healthy weight y for a person whose height is x inches over 4 feet 3 inches. (Thus x=0 corresponds to 4 feet 3 inches and x=9 to 5 feet, ect.)

(b) What is the maximum healthy weight for a person whose height is 5 feet?
pounds 6 feet?
pounds

(c) How tall is a person who is at a maximum healthy weight of 240 pounds?
feet inches.

PLEASE ANSWER IN FULL TEXT, NO IMAGE TEXTS!!!!!!

1 Answer

1 vote

Answer:

The ratio that doubling length while maintaining shape and density increases volume and mass by 2^3 = 8 works in both directions.

Clearly, from what you wrote, the 1600 pound man 12 feet tall would, if shrunk to half size, would way 1/8 of 1600 pounds, or 200 pounds.

The ratio remains consistent. So a 6 foot tall man weighing 200 pounds, reduced equally in all dimensions with no change in bodily density would be 1/2 of 6 feet tall = 3 feet tall and 1/8 of 200 pounds = 25 pounds.

It is easier to understand this if we use a cube, instead of a person. Picture a cubic volume of ice weighing just one pound. That’’s a cube just about 3 inches on each side. For convenience, let’s call 3 inches one unit.

Please visualize the single cube. The initial cube is 1 unit on each side and weighs one pound.Let’s double its linear dimension, keep it a cube and still ice (same density), and see what we get. Visualize this: a cubic block 2 x 2 x 2 units made of 8 cubic blocks., 2 x 2 x 2 units. Doubling the linear size in 3 dimensions increases volume by 2^3 = 8 times, and increases weight by 8 times, as well.

Explanation:

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