Alightning bug flies at a velocity of 0.25 m/s due east toward another lightning bug seen off in the distance. a light easterly breeze blows on the bug at a velocity of 0.25 m/s. what is the resultant velocity of the lightning bug?

Since in this case velocity is a vector quantity, a quantity which has magnitude and direction, therefore the mathematical operations to use here would simply be similar in basic arithmetic.

First let us examine closely the given problem, it stated that the bug is flying at a velocity of 0.25 m / s going east. Taking the east direction as the positive coordinate, therefore the magnitude of the velocity is:

v_bug = + 0.25 m / s

The breeze meanwhile is also blowing due east, therefore the magnitude of the velocity is also:

v_breeze = + 0.25 m / s

To get for the resultant velocity, all we have to do is to add the two velocities:

v_resultant = v_bug + v_breeze

v_resultant = 0.25 m/s + 0.25 m/s

v_resultant = 0.50 m/s

answer: yes, since the line has a steeper rate of change than the exponential the y-values will be greater and they will only intersect one time.

hello from mrbilldoesmath!

answer:   x (x+6)^2, choice b

discussion:

factor x out of the equation:

x^3 + 12x^2 + 36x = x (x^2 + 12x + 36).

note that 6+6 = 12 and 6*6 = 36 so the above factors into:

x (x+6)^2

which is choice b

you,

mrb