Question

(d) use the function v(x)= - 0.2356x² - 0.3038x + 195.3218 to predict the velocity of the fluid at a distance 3.2 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 3.2 cm from the center of the pipe.

Explanation:

Step1: Substitute x value

Substitute \(x = 3.2\) into \(v(x)=- 0.2356x^{2}-0.3038x + 195.3218\).
\[v(3.2)=-0.2356\times(3.2)^{2}-0.3038\times3.2 + 195.3218\]

Step2: Calculate \((3.2)^{2}\)

\((3.2)^{2}=10.24\), then \(v(3.2)=-0.2356\times10.24 - 0.3038\times3.2+195.3218\).

Step3: Calculate multiplications

\(-0.2356\times10.24=-2.412544\), \(-0.3038\times3.2 = - 0.97216\).
\[v(3.2)=-2.412544-0.97216 + 195.3218\]

Step4: Calculate addition and subtraction

\(v(3.2)=(-2.412544-0.97216)+195.3218=-3.384704 + 195.3218 = 191.937096\).

Step5: Round to 1 decimal place

Rounding \(191.937096\) to 1 - decimal place gives \(191.9\).

Answer:

\(191.9\)