<span>the particle's initial position is at t=0, x = 0 - 0 + 4 = 4m
velocity is rate of change of displacement = dx/dt = d(t^3 - 9t^2 +4)/dt
= 3t^2 - 18t
acceleration is rate of change of velocity = d(3t^2 -18t)/dt
= 6t - 18
</span><span>the particle is stationary when velocity = 0, so 3t^2 - 18t =0
</span>3t*(t - 6) = 0
t = 0 or t = 6s
acceleration = 6t - 18 = 0
t = 3s
at t = 3s, velocity = 3(3^2) -18*3 = -27m/s
displacement = 3^3 - 9*3^2 +4 = -50m
Answer:
a. 
Step-by-step explanation:
Since f(x) is the function for the populational density at a certain sidewalk for a 5 mile stretch, a definite integral of that function will yield the total number of people within the integration intervals. If we are interested in the number of people in the whole 5 mile stretch, we must integrate f(x) from x = 0 miles to x = 5 miles:
Therefore, the answer is alternative a.
Is there a picture to show it?
Answer: z=x+2
Step-by-step explanation:
First, find the area of the base (the triangle) and then multiply it by the height
to find the area of the triangle you need to know the height. cut the triangle in half and you get a right triangle, from there you can use the Pythagorean theorem. remember since you cut the triangle in half you have to divide one of the sides by 2
a^2 + b^2 = c^2 (plug in known information)
a^2 + (7.5)^2 = (15)^2 (solve, first solve the exponents)
a^2 + 56.25 = 225 (subtract 56.25 on both sides)
a^2 = 168.75 (solve for a, put 168.75 under the square root)
then once you find the area multiply by the known height
