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>
Answer:
y - y1 = m(x - x1)
(x1, y1) = (1, -1) (x2, y2) = (3, 5)
m = 
m = 
m = 
= 
= 3
m = 3
y - 5 = 3(x - 3)
y - 5 = 3x - 9
y = 3x - 9 + 5
y = 3x - 4
Step-by-step explanation:
In order to use point-slope form to convert to slope-intercept form you have to know one point and the value of the slope. In this case, we know two points, but we don't know the slope. In order to find the slope, you can input the values of the two points into the expression: 
After finding the slope, input the values of one of the points (in this example I used (3,5)) and the slope. After that, multiply the slope by the two terms inside the parentheses. then add 5 to both sides of the equation to isolate y. Now your equation is in slope-intercept form.
I hope this helps :)
Answer:
$79.05
Step-by-step explanation:
Multiply 93 times 15%, which gets you $13.95.
Then subtract 13.95 from the 93 (93 - 13.95).
Answer:
there isnt anything?
Step-by-step explanation:
Answer:
y = 6x - 43
Step-by-step explanation:
(6, -7) and (8,5)
m=(y2-y1)/(x2-x1)
m=(5 + 7)/(8 - 6)
m= 12/2
m = 6
y - y1 = m(x - x1)
y + 7 = 6(x - 6)
y + 7 = 6x - 36
y = 6x - 43
