the formula d=(square root)12,800+h^2 gives the distance d in kilometers to the horizon from a satellite h kilometers above Earth.Find the distance to the horizon to the horizon from a satellite 4200 km above Earth. Round to the nearest kilometer. PLEASE HELP ME
what's the problem? you are given a formula and a value. Plug the value into the formula.
d(h) = √(12800 + h^2)
d(4200) = √(12800+4200^2)
= √(12800+17640000)
= √17652800
= 4201
To find the distance to the horizon from a satellite 4200 km above Earth, we can use the given formula:
d = √(12,800 + h^2)
Substituting the value of h = 4200 into the formula:
d = √(12,800 + 4200^2)
d = √(12,800 + 17,640,000)
d = √17,652,800
d ≈ 4198 km
Rounding to the nearest kilometer, the distance to the horizon from a satellite 4200 km above Earth is approximately 4198 km.
To find the distance to the horizon from a satellite 4200 km above Earth using the formula d = √(12,800 + h^2), where h is the height of the satellite in kilometers, we can substitute the given value of h into the formula and solve for d.
1. Substitute the value of h into the formula: d = √(12,800 + 4200^2).
2. Evaluate the square of 4200: 4200^2 = 17,640,000.
3. Add 12,800 to 17,640,000: 12,800 + 17,640,000 = 17,652,800.
4. Take the square root of 17,652,800: √17,652,800 ≈ 4206.55.
5. Round the result to the nearest kilometer: d ≈ 4207 kilometers.
Therefore, the distance to the horizon from a satellite 4200 km above Earth is approximately 4207 kilometers.