Question

part 1 of 4
(b) 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 40.5 sec to run the length of the pipe at a point 9 cm from the center of the pipe.
part 2 / 4
part 3 of 4
(c) 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(r) =

Explanation:

Step1: Recall quadratic regression formula

The general form of a quadratic function is $v(r)=ar^{2}+br + c$. For regression, if we have data - points $(r_1,v_1),(r_2,v_2),\cdots,(r_n,v_n)$, we can set up a system of equations to find $a$, $b$, and $c$. However, without the given data - points, we assume a general approach. If we use a statistical software or a calculator with regression capabilities (e.g., TI - 84 Plus: enter data into lists, then use the quadratic regression function), we input the values of the independent variable $r$ (distance from the center of the pipe) and the dependent variable $v$ (velocity or some related quantity).
Let's assume we have $n$ data - points. We form the following normal equations based on the least - squares method for quadratic regression:
\[\sum_{i = 1}^{n}v_i=a\sum_{i = 1}^{n}r_i^{2}+b\sum_{i = 1}^{n}r_i+nc\]
\[\sum_{i = 1}^{n}r_iv_i=a\sum_{i = 1}^{n}r_i^{3}+b\sum_{i = 1}^{n}r_i^{2}+c\sum_{i = 1}^{n}r_i\]
\[\sum_{i = 1}^{n}r_i^{2}v_i=a\sum_{i = 1}^{n}r_i^{4}+b\sum_{i = 1}^{n}r_i^{3}+c\sum_{i = 1}^{n}r_i^{2}\]
Since we don't have the actual data - points here, we can't calculate the exact values of $a$, $b$, and $c$. But if we had data - points $(r_1,v_1),(r_2,v_2),(r_3,v_3)$ (for simplicity, $n = 3$), we would substitute $r_1,r_2,r_3$ and $v_1,v_2,v_3$ into the above equations and solve the system of three equations for $a$, $b$, and $c$.

Answer:

Since no data - points are given, we cannot provide a specific quadratic function. If we assume the data - points are entered into a calculator or software for quadratic regression, the general form of the function is $v(r)=ar^{2}+br + c$, and the values of $a$, $b$, and $c$ would be calculated based on the input data.