This is so provided that the velocity changes continuously in which case we can apply the mean value theorem.
<span>Velocity (v) is the derivative of displacement (x) : </span>
<span>v = dx/dt </span>
<span>Monk 1 arrives after a time t* and Monk 2 too. </span>
<span>Name v1(t) and v2(t) their respective velocities throughout the trajectory. </span>
<span>Then we know that both average velocities were equal : </span>
<span>avg1 = avg2 </span>
<span>and avg = integral ( v(t) , t:0->t*) / t* </span>
<span>so </span>
<span>integral (v1(t), t:0->t*) = integral (v2(t), t:0->t*) </span>
<span>which is the same of saying that the covered distances after t* seconds are the same </span>
<span>=> integral (v1(t) - v2(t) , t:0->t*) = 0 </span>
<span>Thus, name v#(t) = v1(t) - v2(t) , then we obtain </span>
<span>=> integral ( v#(t) , t:0->t*) = 0 </span>
<span>Name the analytical integral of v#(t) = V(t) , then we have </span>
<span>=> V(t*) - V(0) = 0 </span>
<span>=> V(t*) = V(0) </span>
<span>So there exist a c in [0, t*] so that </span>
<span>V'(c) = (V(t*) - V(0)) / (t* - 0) (mean value theorem) </span>
<span>We know that V(0) = V(t*) = 0 (covered distances equal at the start and finish), so we get </span>
<span>V'(c) = v#(c) = v1(c) - v2(c) = 0 </span>
<span>=> v1(c) = v2(c) </span>
<span>So there exist a point c in [0, t*] so that the velocity of monk 1 equals that of monk 2. </span>
It helps you determine the characteristics of the plot/graph. I am not sure so it is your choose.
Answer:
-144
Step-by-step explanation:
x=-48 times 3
Answer:
13.8%
Step-by-step explanation:
P = nCr pʳ qⁿ⁻ʳ
P = ₉C₅ (0.37)⁵ (1−0.37)⁹⁻⁵
P ≈ 0.138
Answer:
The bearing needed to navigate from island B to island C is approximately 38.213º.
Step-by-step explanation:
The geometrical diagram representing the statement is introduced below as attachment, and from Trigonometry we determine that bearing needed to navigate from island B to C by the Cosine Law:
(1)
Where:
- The distance from A to C, measured in miles.
- The distance from A to B, measured in miles.
- The distance from B to C, measured in miles.
- Bearing from island B to island C, measured in sexagesimal degrees.
Then, we clear the bearing angle within the equation:
(2)
If we know that 
, 
, 
, then the bearing from island B to island C:
![\theta = \cos^{-1}\left[\frac{(7\mi)^{2}+(8\,mi)^{2}-(5\,mi)^{2}}{2\cdot (8\,mi)\cdot (7\,mi)} \right]](https://tex.z-dn.net/?f=%5Ctheta%20%3D%20%5Ccos%5E%7B-1%7D%5Cleft%5B%5Cfrac%7B%287%5Cmi%29%5E%7B2%7D%2B%288%5C%2Cmi%29%5E%7B2%7D-%285%5C%2Cmi%29%5E%7B2%7D%7D%7B2%5Ccdot%20%288%5C%2Cmi%29%5Ccdot%20%287%5C%2Cmi%29%7D%20%5Cright%5D)
The bearing needed to navigate from island B to island C is approximately 38.213º.
