Find dy in the following cases:
dx
(i) x = 2at,
y = at2​

Sorry if i'm wrong, I'm still half confused by what you mean in this question.

if you mean to find the derivative when x=2*at and y=(at)^2 then y=(x/2)^2 and the implicit derivative d/dx (y) is x/2. If you could post a screenshot or a picture of the actual problem I think it will help.

speed of plane is 720 km/h

Speed of wind is 80km/h

Step-by-step explanation:

Let x represent the speed of the plane.

Let y represent the speed of the wind.

The plane flies from Atlanta to los Angeles and against the wind in 5hrs and the distance between Atlanta and los Angeles is 3200 km.

Since it flew against the wind, the speed would be x-y km/hour

Distance = speed × time. Therefore

3200 = 5(x - y )

3200 = 5x - 5y - - - - - - - - - 1

the return trip back to Atlanta with the wind only 4 hr. This means that the speed is x+y km/hour. Therefore

3200 = 4(x+y)

3200 = 4x + 4y - - - - - - - - 2

Multiplying equation 1 by 4 and equation 2 by 5, it becomes

12800 = 20x - 20y

16000 = 20x - 20y

Adding both equations, it becomes

28800 = 40x

x = 28800/40 = 720

Substituting x = 720 into 3200 = 5(x - y )

x - y = 3200/5 = 640

y = 720 - 640 = 80