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An object’s weight depends on its height above the surface of the earth. If a man weighs 190 pounds on the surface of the earth, then the man's weight in pounds (W) x miles above the surface is approximated by the formula:

W = (190⋅4,000^2) / (4,000+x)^2

For each problem below, approximate the weight of a 190-pound person at the given height above the surface of the earth.

Remember, 1 mile = 5,280 feet.

1. 100 miles

2. 1,000 miles

3. 1,056,000 feet

4. 10,000,000 feet

my work 180 pds 121.6 pds 172 pds around 87 pds

## 1.180 2.121.6 3.172 4.around 87 pounds

## 1. I got 180.8 which would round to 181

2. yup

3. 172.3356

4. 87.5

Were you rounding off before you got to the last answers?

## To solve each problem, we can substitute the given height value (in miles or feet) into the provided formula to approximate the weight of a 190-pound person at that height.

1. To approximate the weight 100 miles above the surface of the earth:

Substitute x = 100 into the formula:

W = (190 * (4,000^2)) / (4,000+100)^2

= (190 * 16,000,000) / (4,100)^2

= 3,040,000,000 / 16,810,000

≈ 180.98 pounds (rounding to two decimal places)

2. To approximate the weight 1,000 miles above the surface of the earth:

Substitute x = 1,000 into the formula:

W = (190 * (4,000^2)) / (4,000+1,000)^2

= (190 * 16,000,000) / (5,000)^2

= 3,040,000,000 / 25,000,000

≈ 121.6 pounds (rounding to one decimal place)

3. To approximate the weight 1,056,000 feet above the surface of the earth:

Convert 1,056,000 feet to miles by dividing by 5,280:

1,056,000 feet / 5,280 = 200 miles

Substitute x = 200 into the formula:

W = (190 * (4,000^2)) / (4,000+200)^2

= (190 * 16,000,000) / (4,200)^2

= 3,040,000,000 / 17,640,000

≈ 172.33 pounds (rounding to two decimal places)

4. To approximate the weight 10,000,000 feet above the surface of the earth:

Convert 10,000,000 feet to miles by dividing by 5,280:

10,000,000 feet / 5,280 = 1,893.94 miles

Substitute x = 1,893.94 into the formula:

W = (190 * (4,000^2)) / (4,000+1,893.94)^2

= (190 * 16,000,000) / (5,893.94)^2

= 3,040,000,000 / 34,745,372.01

≈ 87.52 pounds (rounding to two decimal places)

Therefore, the approximate weights of a 190-pound person at the given heights are as follows:

1. 180.98 pounds

2. 121.6 pounds

3. 172.33 pounds

4. 87.52 pounds