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By taking pi=3.141, evaluate (2pi+3sqrt(...

By taking `pi=3.141`, evaluate `(2pi+3sqrt(2))/(5)` upto three places of decimal.

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To evaluate the expression \((2\pi + 3\sqrt{2}) / 5\) using \(\pi = 3.141\) and \(\sqrt{2} = 1.414\), follow these steps: ### Step 1: Substitute the values of \(\pi\) and \(\sqrt{2}\) We know: \[ \pi = 3.141 \quad \text{and} \quad \sqrt{2} = 1.414 \] Now substitute these values into the expression: \[ 2\pi + 3\sqrt{2} = 2(3.141) + 3(1.414) \] ### Step 2: Calculate \(2\pi\) Calculate \(2\pi\): \[ 2 \times 3.141 = 6.282 \] ### Step 3: Calculate \(3\sqrt{2}\) Calculate \(3\sqrt{2}\): \[ 3 \times 1.414 = 4.242 \] ### Step 4: Add the results from Step 2 and Step 3 Now add the results: \[ 6.282 + 4.242 = 10.524 \] ### Step 5: Divide by 5 Finally, divide the sum by 5: \[ \frac{10.524}{5} = 2.1048 \] ### Step 6: Round to three decimal places Rounding \(2.1048\) to three decimal places gives: \[ 2.105 \] ### Final Answer Thus, the value of \((2\pi + 3\sqrt{2}) / 5\) up to three decimal places is: \[ \boxed{2.105} \]
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