(Modeling) Distance from the Origin of the Nile River The Nile...

Question

(Modeling) Distance from the Origin of the Nile River The Nile River in Africa is about 4000 mi long. The Nile begins as an outlet of Lake Victoria at an altitude of 7000 ft above sea level and empties into the Mediterranean Sea at sea level (0 ft). The distance from its origin in thousands of miles is related to its height above sea level in thousands of feet (x) by the following formula.

Distance = (7 − x) / (0.639x + 1.75)

For example, when the river is at an altitude of 600 ft, x = 0.6 (thousand), and the distance from the origin is

Distance ≈ (7 − 0.6) / (0.639 × 0.6 + 1.75) ≈ 3, which represents 3000 mi. (Data from The World Almanac and Book of Facts.) What is the distance from the origin of the Nile when the river has an altitude of 7000 ft?

Accepted Answer

Hello, everyone we are told on a certain planet the external pressure an alien feels as it vertically transverses from the surface to space is defined by the formula below. We are given P sub ext equals 10 minus H divided by 0.428 H plus 7.545 where H is the vertical distance from the surface of the planet every 10,000 m. And P sub ext is measured in atmospheres abbreviated ATM. This formula only holds true if H is measured from the surface to the boundary between the planet and the space or sorry, the planet and space theorized to not exceed 100 kilometers. Hence H can equal zero but has to fall between zero and 10. We want to calculate the external pressure that an alien experiences. If it is 83,000 m from the surface. Our answer choices are a 1.154 atmospheres, B 0.153 atmospheres, C 1.004 atmospheres D 0.953 atmospheres. So before we use the formula itself, let's find H so if H is measured every 10,000 m from the surface of the planet. And we are told that right now, we want to calculate when an alien is 83,000 m from the surface of the planet, we calculate H by doing 83,000, divided by 10,000. So this will tell us how many our H is. And when we do this division, we get 8.3 we should quickly check to make sure that it falls within our constraints. H has to be between or equal to zero and less than 10, 8.3 is less than 10 and greater than zero. So this works. So now we're gonna put this into our formula. So we have P sub ext equals minus H which we just discovered is 8. divided by 0. multiplied by 8.3 plus 7.545. So I'm gonna simplify what I can in my numerator 10 minus 8.3 is gonna be 1. in the denominator. When I multiply 0.428 by 8.3 I get 3.5524 still plus 7.545. I'm gonna combine my like terms of my denominator. So I have 1.7 divided by 11.0974. And when I do the division, I have P sub ext equals 0.15319. Um It looks like all of our answer choices are rounded to three decimal places. So we'll put that as 0. atmospheres. So this is the external pressure that an alien would feel at 83,000 m from the surface answer. Choice B 0.153 atmospheres have a nice day.

Key Concepts

Understanding the Given Formula

Unit Conversion and Scaling

Evaluating Rational Expressions

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