An airplane is flying at a speed of 350 mi/h at an altitude of one mile and passes directly over a radar station at time t=0.

a) Express the horizontal distance d (in miles) that the plane has flown as a function of t.

I really don't know... would it be something like d= t . a + b?

b) Express the distance s between the plane and the radar station as a function of d.

c) Use composition to express s as a function of t.

a) To find the horizontal distance, d, that the plane has flown as a function of time, t, we need to take into account the plane's speed. The formula to calculate distance is speed multiplied by time. In this case, the plane is flying at a speed of 350 mi/h, so the function can be expressed as:

d = 350t

b) To express the distance, s, between the plane and the radar station as a function of d, we need to consider the altitude of the plane. Since the plane passes directly over the radar station at an altitude of one mile, the hypotenuse of the right triangle formed by the altitude and the distance is constant. Therefore, using the Pythagorean theorem, we can express s as:

s = √(d^2 + 1)

c) By applying composition, we can express s as a function of t. We substitute the expression for d from part (a) into the function in part (b):

s = √((350t)^2 + 1)

To answer these questions, you can use the basic relationships between distance, speed, time, and altitude.

a) Expressing the horizontal distance d (in miles) that the plane has flown as a function of t:

We can assume that the airplane is flying horizontally, so the distance it has flown is the same as the distance it has traveled in the x-axis.

We know that the airplane is flying at a constant speed of 350 mi/h. Hence, the distance traveled is given by:

d = speed * time

Since the plane passes directly over the radar station at time t=0, we can express the horizontal distance d as:

d(t) = 350t

So, the horizontal distance d (in miles) that the plane has flown is given by d(t) = 350t.

b) Expressing the distance s between the plane and the radar station as a function of d:

The distance s is the vertical distance between the plane and the radar station, which is the altitude. We are given that the altitude is one mile, so the distance s is constant:

s = 1 mile

So, the distance s (in miles) between the plane and the radar station is given by s = 1.

c) Using composition to express s as a function of t:

To express s as a function of t, we substitute the value of d(t) into the expression for s. From part a), we know that d(t) = 350t.

So, substituting d(t) into the expression for s:

s(t) = 1

So, the distance s between the plane and the radar station is a constant 1 mile, regardless of the time t.

In summary:
a) The horizontal distance d that the plane has flown is given by d(t) = 350t (in miles).
b) The distance s between the plane and the radar station is given by s = 1 mile.
c) The distance s can also be expressed as s(t) = 1, indicating that the distance between the plane and the radar station remains constant at 1 mile throughout the flight.

since distance = rate x time

d = 350t

now look at your triangle. It is right-angled with a height of 1, a horizontal distance of d and the hypotenuse is s

s^2 = 1^2 + d^2 , but d = 350t
so....
s^2 = 1 + (350t)^2
s = √(1 + 122500t^2)