Fluid runs through a drainage pipe with a 10-cm radius and a length of 25 m (2500 cm). The velocity of the fluid gradually decreases from the center of the pipe ttoward the edges as a result of friction with the walls of the pipe. For the data shown, v(x) is the velocity of the fluid (in cm/sec) and x represents the distance (in ccm) from the center of the pipe toward the edge. 0-195.2,1-194.7,2-193.7,3-192.3,4-190.6,5-188.4,6-185.8,7-182.8,8-179.5,9-175.7

The pipe is 25 m long (2500 cm).

1. Determine how long it will take fluid to run the length of the pipe through the center of the pipe. Round to 1 decimal place.

It will take fluid approximately sec to run the length of the pipe through the center of the pipe.

2.Determine how long it will take fluid at a point 9 cm from the center of the pipe to run the length of the pipe. Round to 1 decimal place.

It will take fluid approximately sec to run the length of the pipe at a point 9 cm from the center of the pipe.

3.Use regression to find a quadratic function to model the data. Use all of the given data points and round each coefficient to 4 decimal places.

The function is v(x)=

4. Use the function v(x)=0.2008x^2-0.3635x +195.2273 to predict the velocity of the fluid at a distance 5.1 cm from the center of the pipe. Round to 1 decimal place. The velocity of the fluid will be approximately cm/sec at a distance of 5.1 cm from the center of the pipe.