(2m west) + (3m south) + (4m east) + (1m north) =
[ (2m west)+(4m east) ] + [ (3m south)+(1m north) ] =
[ (-2m east)+(4m east) ] + [ (3m south)-(1m south) ] =
(2m east) + (2m south)
Now, so far, we have the orthogonal (perpendicular) components of the displacement ... the North/South component and the East/West component.
To combine these, it's time for Pythagoras:
Displacement = √[ (2m)² + (2m)² ]
Displacement = √ (4m² + 4m²)
Diplacement = √8m²
<em>Displacement = 2.83 meters Southeast</em>
Mathematics<span> is </span>important to science<span> because when </span>scientific findings in nature are expressed mathematically, they are easier to verify or disprove by experiment. <span>Without mathematics we would ultimately have no nice way of understanding or analyzing the relationships between quantities we observe and measure.</span>
Answer:
1) 
2)
Explanation:
Given data:
speed of sound v = 1540 m/s
frequency f = 1.40 MHz = 1.40 \times 10^6 Hz
density 
1) we know that
2) we know that
v1f = -0.16 ms
Explanation:
Use the conservation law of linear momentum:
m1v1i + m2v2i = m1v1f + m2v2f
where
v1i = v2i = 0
m1 = 160 kg
m2 = 0.50 kg
v2f = 50m/s
v1f = ?
So we have
0 = (160 kg)v1f + (0.5 kg)(50 m/s)
v1f = -(25 kg-m/s)/(160 kg)
= -0.16 m/s
Note: the negative sign means that its direction is opposite that of the arrow.
The gravitational pull on moon A will be lower since it is further away from the new planet.
