An air traffic controller spots two airplanes at the same altitude converging to a point as they fly at right angles to each oth
er. One airplane is 70 miles from the point and has a speed of 420 miles per hour. The other is 240 miles from the point and has a speed of 1440 miles per hour.
(a) At what rate is the distance between the planes changing? in mph?
(b) How much time does the controller have to get one of the airplanes on a different flight path?
(a) At what rate is the distance between the planes changing? in mph?
(b) How much time does the controller have to get one of the airplanes on a different flight path?
2 answers:
Answer:
(a) ðz/ðt = 1500miles/hr
(b) 10minutes
Step-by-step explanation:
Let x rep plane one
Let y rep plane two
ðx/ðt = 1440miles/hr = speed of plane one
ðy/ðt = 420miles/hr = speed of plane 2
ðz/ðt = ? = rate of change of distance btw two plane moving at right angle to meet at point o...
See attachment
Since x² + y² = z²... equation 1
So therefore (240² + 70²) ^½= z = 250 miles = distance between two planes
Differential rate of equation 1 gives
(2x* ðx/ðt ) + (2y* ðy/ðt) = 2z* ðz/ðt
Substituting to get ðz/ðt
(2*240*1440) + (2*70*420) = 2*250*ðz/ðt
750000 = 500 ðz/ðt
ðz/ðt = 1500miles/hr
B.
Since v = d/t where d = distance = 250miles
t = time = ? = time needed for controller to divert one of e planes , v = 1500miles/hr
t = d/v = 250/1500 = 10minutes
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Answer:
A) find its center = (3, 2)
B) find the radius of the circle = √104
C) find the equation of the circle = x² + y² - 6x - 4y -91 = 0
Step-by-step explanation:
A)- The center must be the mid-points of (-2, 1) and (8, 3).
So, using the equation of mid-point,
Here, (x₁, y₁) = (-2, 1) and (x₂, y₂) = (8, 3)
Putting these value in above equation. We get,
h = 3 and k = 2
Thus, Center = (h, k) = (3, 2)
B)- For finding the radius we have to find the distance between center and any of the end point.
Thus using Distance Formula,
⇒ Radius = √104 = 2√26
C)- The equation of circle is determined by formula:
where (h, k ) is center of circle and
r is the radius of circle.
⇒ (x - 3)² + (y - 2)² = 104
⇒ x² + y² - 6x - 4y -91 = 0
which is the required equation of the circle.