please I need the correct answer I am reasking, it was marked wrong with 12.09 and I don't know what to do The velocity of a particle moving along a line is a function of time given by\[ v(t) = \frac{79}{t^2 + 12t + 27} \]Find the distance, in feet, that the particle has traveled after $ t = 1 $ seconds. Assume the particle started at $ t = 0 $ seconds. *Round the results to 2 decimal places.**[Text Box]*

Answered: The velocity of a particle moving along…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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please I need the correct answer I am reasking, it was marked wrong with 12.09 and I don't know what to do

The velocity of a particle moving along a line is a function of time given by

\[ v(t) = \frac{79}{t^2 + 12t + 27} \]

Find the distance, in feet, that the particle has traveled after $ t = 1 $ seconds. Assume the particle started at $ t = 0 $ seconds. *Round the results to 2 decimal places.*

*[Text Box]*

Expert Solution

Step 1: The given data is:

The velocity of a particle moving along a line is a function of time is given by,

$table row cell straight v open parentheses straight t close parentheses end cell equals cell fraction numerator 79 over denominator straight t squared plus 12 straight t plus 27 end fraction end cell row cell straight v open parentheses straight t close parentheses end cell equals cell fraction numerator 79 over denominator open parentheses straight t plus 3 close parentheses open parentheses straight t plus 9 close parentheses end fraction end cell end table$

Find the distance, in feet, that the particle has traveled after $straight t equals 1 space seconds space$

Given particle started at $straight t equals 0 space seconds$