Mathematics
14.08.2020 04:12
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What is the coefficient of the variable in the expression 2-5x-4+8?

What is the coefficient of the variable in the expression 2-5x-4+8?
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drewdean5545
drewdean5545
4,5(74 marks)
-5x+6

Coefficient is -5 and 6, respectively.
jeterboi
jeterboi
4,9(40 marks)
This is so provided that the velocity changes continuously in which case we can apply the mean value theorem. 
Velocity (v) is the derivative of displacement (x) : 
v = dx/dt 
Monk 1 arrives after a time t* and Monk 2 too. 
Name v1(t) and v2(t) their respective velocities throughout the trajectory. 
Then we know that both average velocities were equal : 
avg1 = avg2 
and avg = integral ( v(t) , t:0->t*) / t* 
so 
integral (v1(t), t:0->t*) = integral (v2(t), t:0->t*) 
which is the same of saying that the covered distances after t* seconds are the same 
=> integral (v1(t) - v2(t) , t:0->t*) = 0 
Thus, name v#(t) = v1(t) - v2(t) , then we obtain 
=> integral ( v#(t) , t:0->t*) = 0 
Name the analytical integral of v#(t) = V(t) , then we have 
=> V(t*) - V(0) = 0 
=> V(t*) = V(0) 
So there exist a c in [0, t*] so that 
V'(c) = (V(t*) - V(0)) / (t* - 0) (mean value theorem) 
We know that V(0) = V(t*) = 0 (covered distances equal at the start and finish), so we get 
V'(c) = v#(c) = v1(c) - v2(c) = 0 
=> v1(c) = v2(c) 
So there exist a point c in [0, t*] so that the velocity of monk 1 equals that of monk 2. 

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