Cstem2003idn
Answered

Uncover valuable information and solutions with IDNLearn.com's extensive Q&A platform. Discover the information you need from our experienced professionals who provide accurate and reliable answers to all your questions.

The position s(t) of a robot moving along a track at time t is given by s(t)=9t^2−90t+4.
Find the total distance traveled by the robot from t=0 to t=9.

Sagot :

Raphealnwobiidn

The total distance traveled by the robot from t=0 to t=9 is 1422 units

Integration is a way in which smaller components are brought together in pieces to form a whole. Integration can be used in finding areas, volumes and so on.

Given that the position s(t) at any time t is given by the function:

s(t)=9t²−90t+4

The total distance traveled by the robot from t=0 to t=9 can be gotten by integrating the position function within the limits 0< t < 9

Therefore:

[tex]Total\ distance = \int\limits^9_0 {s(t) \, dt \\\\Total\ distance = \int\limits^9_0 {(9t^2-90t+4) \, dt\\\\Total\ distance = [3t^3-45t+4t]_0^9\\\\Total\ distance=-1422\ units[/tex]

The total distance is 1422 units

Find out more at: https://brainly.com/question/22008756

Thank you for being part of this discussion. Keep exploring, asking questions, and sharing your insights with the community. Together, we can find the best solutions. Find reliable answers at IDNLearn.com. Thanks for stopping by, and come back for more trustworthy solutions.