With a given head wind, a plane can fly 3000 km in 6 hours. flying in the opposite direction with the same wind blowing, the plane can fly the same distance in 5 hours. find the planes air speed and the speed of the wind.

Air speed of plane

Speed of wind

Step-by-step explanation:

Given:

Distance = 3000 km

Time, the plane takes to cover the distance opposite wind direction= 6 hours

Time, the plane takes to cover the distance in wind direction= 5 hours

∴ Speed in opposite wind direction

∴ Speed in windward direction

Let air speed of plane be

Let speed of wind be

Speed in opposite wind direction

Speed in wind direction is

Substituting the known values, we can get two equations.

1)

2)

Adding the above equations we get:

dividing both sides by 2.

∴

Substituting the value of in equation (2) to find

we get

Subtracting both sides by 550.

∴

Air speed of plane

Speed of wind

146%

step-by-step explanation:

f(2x−x2)=−3x2+6x−1

step-by-step explanation:

set up the composite function and evaluate.

f(2x−x2)=−3x2+6x−1