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:
45 in
Step-by-step explanation:
This look like the branch of the basic pythagorean triplet.
3, 4, 5 is a fundamental triplet.
if you multiply all three numbers by 9, you will get:
27, 36, 45
X = 45 in
Hope this helps :)
It is simple
Step 1) substitute x = 5 into the equation
3x +4
3(5) + 4 gives you 3 times 5 + 4
The answer is 15 + 4 which is 19
Now substitute a and b into the equation 3(a) + 4(b) when the a = 6 and b = 5
Hereby 3(6) + 4(5)
3 * 6 = 18 and 4* 5 = 20
18 + 20 = 38
The answer is 38
Now finally
Substitute a and b Into the equation
3(3) + 4(6)
9+ 24 = 33
If given the equation, you need to take the number beside the x and y and change their signs to get your point:
x - 8 (Take the -8 and make it +8)
y + 2 (Take the +2 and make it -2)
Your point is (8, -2)
Follow PEMDAS
multiplication is first (in this case) and then addition
2 x 8 = 16
16 + 2 = 18
18 is your answer
hope this helps
