Answer:
562.23
Step-by-step explanation:
Simplify 2 x - 8 x - 6 y + 9 -14 + x + 11 y.
2 answers:
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A function is a relationship that maps each member of a set of input values into only one member of the set of output values
The correct values for the costs per passenger are as follows:
(a) At 470 miles per hour, the cost is approximately <u>$189.48 per passenger</u>
At 590 miles per hour, the cost is approximately <u>$191.9 per passenger</u>
(b) The <em>domain </em>of the function <em>C </em> is <u>0 < x ≤ ∞</u>
(c) Please find attached the required graph
(d) The table is included in the solution
(e) The <em>ground speed</em> that minimizes the cost per passenger is <u>500 miles per hour</u>
The reason the above values are correct is as follows:
The known parameters are;
The <em>length </em>of the Atlantic ocean the airplane crosses<em> = 3,000 miles</em>
The airspeed with which the airplane crosses the Atlantic ocean <em>= 500 mi/hr</em>
The given function that gives the cost per passenger is presented as follows;
Where x is the ground speed of the airplane = airspeed ± windspeed
(a) Required:
(i) The cost when the ground speed is <em>470 miles per hour</em>
Solution:
The cost C, when the ground speed is <em>470 miles per hour</em> is approximately <u>$189.48 per passenger</u>
(ii) The cost when the ground speed is <em>590 miles per hour</em>
Solution:
The cost C, when the ground speed is <em>590 miles per hour</em> is approximately <u>$191.9 per passenger</u>
(b) Required:
To find the domain of <em>C</em>
The domain of a function is given by the values of the function for which the function is defined, or possible, or for which there is an output
Given that the independent variable, <em>x</em>, is a denominator, we have that the function is not defined (<em>Does not exist</em>) at <em>x = 0</em>
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The domain of the function <em>C </em> is 0 < x ≤ ∞
c) Required:
Graph the function using a graphing calculator
Please find attached the required graph of the function created with MS Excel
(d) Required:
(i) To create a table of values for the groundspeed
Please find the required TABLE as follows
(e) Required:
<em>To find the required ground speed</em> that gives the minimum cost per passenger
Solution:
By differentiation, we get;
Which gives;
7·x² - 1666000 = 0
7·x² = 1666000
x = √(1666000/7) ≈ 487.85
Therefore, to the nearest 50 miles per hour, the ground speed that minimizes the cost per passenger is <u>500 miles per hour</u>
Learn more about functions here:
