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>
Hello! The forula for compound inerest is P(1 + r)^t, where P = principal, r = rate, and t = time in years. The rate is 6.75% is 0.0675 in decimal form. Let's add 1 to that number in order to get 1.0675. The time amount is 8 years, so we will raise that number to the 8th power. 1.0675^8 is 1.686331954 This is a long decimal, but do not delete it from your calculator. Now, we multiply that by the principal, which is 1,425. When you do, you get 2,403.023035 or 2,403.02 when rounded to the nearest hundredth. The total amount after 8 years is $2,403.02.
Answer:
enjoy it .................
Answer:
P.E.M.D.A.S.
Step-by-step explanation:
P. Parenthesis
E. Exponents
M. Multipacation
D. Division
A. Addition
S. Subtraction