Hello everyone, I'm having some trouble getting started with this problem because I think I misunderstand the meaning. Can anyone help me? I'm confident I'll be able to complete the problem once I finish step 1, I just don't understand what it's asking? How can you design a function to measure the amount of time required to move a single foot when the variable of the function that you provide is the number of feet traveled? It doesn't make sense to me.
When an aircraft attempts to climb as rapidly as possible, its climb rate (in feet per minute) decreases as altitude increases, because the air is less dense at higher altitudes. Given below is a table showing performance data for a certain single engine aircraft, giving its climb rate at various altitudes, where c(h) denotes the climb rate of the airplane at an altitude h.
1) Define a new function m(h) that measures the number of minutes required for a plane at altitude h to climb to the next foot of altitude.
2) Construct a table similar to the one above for the values of m(h) and explain how it is related to the table above. Be sure to explain the units.
3) Give a careful interpretation of a function whose derivative is m(h). Describe what the input is and what the output is. Also, explain in plain English what the function tells us.
4) Determine a definite integral whose value tells us exactly the number of minutes required for the airplane to ascend to 10,000 feet of altitude. Clearly explain why the value of this integral has the required meaning.
5) Use the Riemann sum M5 to estimate the value of the integral you found in (c). Include units on your result.
When an aircraft attempts to climb as rapidly as possible, its climb rate (in feet per minute) decreases as altitude increases, because the air is less dense at higher altitudes. Given below is a table showing performance data for a certain single engine aircraft, giving its climb rate at various altitudes, where c(h) denotes the climb rate of the airplane at an altitude h.
| h(feet) | 0 | 1,000 | 2,000 | 3,000 | 4,000 | 5,000 | 6,000 | 7,000 | 8,000 | 9,000 | 10,000 |
| c(h) (ft/min) | 925 | 875 | 830 | 780 | 730 | 685 | 635 | 585 | 535 | 490 | 440 |
2) Construct a table similar to the one above for the values of m(h) and explain how it is related to the table above. Be sure to explain the units.
3) Give a careful interpretation of a function whose derivative is m(h). Describe what the input is and what the output is. Also, explain in plain English what the function tells us.
4) Determine a definite integral whose value tells us exactly the number of minutes required for the airplane to ascend to 10,000 feet of altitude. Clearly explain why the value of this integral has the required meaning.
5) Use the Riemann sum M5 to estimate the value of the integral you found in (c). Include units on your result.
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