The displacement vector a and b when added together , give the resultant vector r so that r= a+b use the data in the drawing and the fact that phi: 25 ^*degrees* to find the magnitude r of the resultant vector and the angle that it makes with the x-axis

The addition of vectors involve both magnitude and direction. In this case, we make use of a triangle to visualize the problem. The length of two sides were given while the measure of the angle between the two sides can be derived. We then assign variables for each of the given quantities.

Let:

b = length of one side = 8 m
c = length of one side = 6 m
A = angle between b and c = 90°-25° = 75°

We then use the cosine law to find the length of the unknown side. The cosine law results to the formula: a^2 = b^2 + c^2 -2*b*c*cos(A). Substituting the values, we then have: a = sqrt[(8)^2 + (6)^2 -2(8)(6)cos(75°)]. Finally, we have a = 8.6691 m.

Next, we make use of the sine law to get the angle, B, which is opposite to the side B. The sine law results to the formula: sin(A)/a = sin(B)/b and consequently, sin(75)/8.6691 = sin(B)/8. We then get B = 63.0464°. However, the direction of the resultant vector is given by the angle Θ which is Θ = 90° - 63.0464° = 26.9536°.

In summary, the resultant vector has a magnitude of 8.6691 m and it makes an angle equal to 26.9536° with the x-axis.
 

Domain eukarya; kingdom plantae should be the answer.

Sounds propagates through some kind of medium. usually it's air, but it goes just as well through solid objects like walls, windows etc. a soundwave will compress the (air)molecules in front of it, and if this increased density wave hits your ears, you register it as sound. solid objects like walls are a lot denser than air, this means that they will damp a wave, but also carry it easier.