You must submit your response as a file.

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