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>
x + x + 1 + x + 2 + x + 3 = 130
Combine like terms.
4x + 6 = 130
Subtract 6 from both sides.
4x = 124
Divide both sides by 4.
x = 31
<h3>The first digit is 31.</h3><h3>The second is 32.</h3><h3>The third is 33.</h3><h3>The fourth if 34.</h3>
Answer:
a) P(X<50)=0.9827
b) P(X>47)=0.4321
c) P(-1.5<z<1.5)=0.8664
Step-by-step explanation:
We will calculate the probability based on a random sample of one moped out of the population, normally distributed with mean 46.7 and standard deviation 1.75.
a) This means we have to calculate P(x<50).
We will calculate the z-score and then calculate the probability accordign to the standard normal distribution:
b) We have to calculatee P(x>47).
We will calculate the z-score and then calculate the probability accordign to the standard normal distribution:
c) If the value differs 1.5 standard deviations from the mean value, we have a z-score of z=1.5
So the probability that maximum speed differs from the mean value by at most 1.5 standard deviations is P(-1.5<z<1.5):
The answer is B:40 hours. You take 200 divided by 20 to get 10 (the amount of 20 page sections he needs to read) and then multiply 10 by 4 (the speed he reads).
Powers of ten! is the answer
