Acyclist rides 3 km west and then turns around and rides 2 km east. (a) what is his displacement? (b) what is the distance traveled? (c) what is the magnitude of his displacement?

Hey there!!

TERMS -

Displacement - the shortest distance from the starting to the ending point

Distance - Longest point .

Now, a person walks 3 km to the west and from there to the 2 km east

The diagram would like :

If we take a starting point anywhere, the line or the distance would travel to the left and then from the walker's perspective, we will have to turn east. From our perspective it would be the line going up.

After we have drawn the figure, it would have a base and  a leg, remember, this is a right angle triangle

The base = 3 km

The leg = 2 Km

Displacement = hypotenuse

Use the Pythagorean theorem

c² = a² + b²

where c = hypotenuse , a = base , b = leg or the height

c² = ( 3 )² + ( 2 )²

c² = 9 + 4

c² = 13

c = √13

c = 3.6

Hypotenuse = 3.6

Displacement = 3.6 Km

Distance = longest

How do we find it?

add up the sides from the starting point to the destination

= 3 + 2

= 5 KM

Distance = 5 Km

Magnitude of displacement - North-East

Hope my answer helps!

f(2x−x2)=−3x2+6x−1

step-by-step explanation:

set up the composite function and evaluate.

f(2x−x2)=−3x2+6x−1

it would be 6xy and -16xy.