To express: The horizontal distance (in miles) covered by a plane as a function of time t.
The function that represents the horizontal distance in terms of time t is .
The plane is flying at a speed of 350 mi/h and at an altitude of one mile.
The plane passes the radar station at time .
Let the horizontal distance be d.
Substitute t for time and 350 for speed in the distance formula, .
Thus, the function is where d(t) is measured in miles.
Therefore, the horizontal distance covered by the plane after t hours is .
To express: The distance (s) between the plane and radar station in terms of d.
The function that represents the distance between the plane and radar station in terms of the distance d is .
Let the horizontal distance be d in mi/hr.
It is given that the altitude is 1 mile.
Use the Pythagoras formula and obtain the value of s as follows.
Thus, the function is where s(d) is measured in miles.
Therefore, the distance between the plane and radar station as a function of d is .
To find: The expression for .
The value of .
The composite function is defined as .
From part (a), the value of .
Substitute for d in ,
Thus, the required composition function, .
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