A particle moves along the x-axis. The velocity of the particle at time t is −2t+8 . What is the total distance traveled by the particle from t=1 to t=6?

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Step-by-step explanation:

The velocity is given by:

And the total distance given the velocity is given by:

So, the total distance traveled by the particle from t = 1 to t = 6 will be:

The absolute value tells us that:

So, split the integral into two parts:

Integrate:

Evaluate:

step-by-step explanation:

let

we know that

the y-intercept is the y-coordinate of the point when the value of x is equal to zero

so

the y-coordinate of the point a is the y-intercept

the answer part a) is

the value of y-intercept is

part b) find the slope m

we know that

the value of the slope is equal to

substitute the values

therefore

the answer part b) is

the value of the slope is equal to

the general answer is

the slope is

the value of y-intercept is

not only in mathematics, scientific proof also are required in the other field of science. also maths proofs are of particular structure, containing steps and logics. so proving is like doing science, it is science. that's why it is important to prove. 

an inaccurate proof leads to errors, or stating results that are not accurate.  which wil mess the probelm up you dont want this