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Sagot :
Let's solve the table of mathematical expressions step-by-step, as outlined below:
[tex]\[ \begin{array}{|c|c|c|c|c|c|} \hline \multicolumn{6}{|c|}{\text{Mathematical Expressions}} \\ \hline \text{Start Here} & -3 & \sqrt{7} & 4.25 & \sqrt{144} & \frac{3}{10} \\ \hline \frac{\sqrt{3}}{2} & \frac{6}{3} & 2.95 & 2 \frac{2}{3} & \pi & 0.33333 \\ \hline \pi + 3 & \sqrt[3]{9} & 0.12323 & 3 + \sqrt{71} & \frac{2}{0} & \frac{5}{2} \\ \hline \frac{0}{2} & -31 & 3 + \sqrt{81} & 3^2 & 2 - 3 & 0 - 4 \\ \hline 2^3 & 3 \pi & 9.89012 & 1.12112 & 5 - \sqrt{3} & 9.23242 \\ \hline \frac{4}{3} & 4 \sqrt{5} & 4 \sqrt{4} & \sqrt[3]{8} & 9 & \sqrt{5} \\ \hline - \frac{2}{4} & -\sqrt{9} & 3 - \frac{3}{4} & 6 \sqrt{3} & -\frac{25}{37} & \text{End Here} \\ \hline \end{array} \][/tex]
Now, we'll solve these expressions one by one:
First Row:
1. -3 (This is a given constant)
2. [tex]\(\sqrt{7} \approx 2.6457513110645907\)[/tex]
3. 4.25 (This is a given constant)
4. [tex]\(\sqrt{144} = 12.0\)[/tex]
5. [tex]\(\frac{3}{10} = 0.3\)[/tex]
Second Row:
1. [tex]\(\frac{\sqrt{3}}{2} \approx 0.8660254037844386\)[/tex]
2. [tex]\(\frac{6}{3} = 2.0\)[/tex]
3. 2.95 (This is a given constant)
4. [tex]\(2 \frac{2}{3} = 2 + \frac{2}{3} = 2.6666666666666665\)[/tex]
5. [tex]\(\pi \approx 3.141592653589793\)[/tex]
6. 0.33333 (This is a given constant)
Third Row:
1. [tex]\(\pi + 3 \approx 6.141592653589793\)[/tex]
2. [tex]\(\sqrt[3]{9} \approx 2.080083823051904\)[/tex]
3. 0.12323 (This is a given constant)
4. [tex]\(3 + \sqrt{71} \approx 11.426149773176359\)[/tex]
5. [tex]\(\frac{2}{0}\)[/tex] (Division by zero is undefined, so we use NaN which stands for Not a Number)
6. [tex]\(\frac{5}{2} = 2.5\)[/tex]
Fourth Row:
1. [tex]\(\frac{0}{2} = 0.0\)[/tex]
2. -31 (This is a given constant)
3. [tex]\(3 + \sqrt{81} = 3 + 9 = 12.0\)[/tex]
4. [tex]\(3^2 = 9\)[/tex]
5. 2 - 3 = -1
6. 0 - 4 = -4
Fifth Row:
1. [tex]\(2^3 = 8\)[/tex]
2. [tex]\(3 \pi \approx 9.42477796076938\)[/tex]
3. 9.89012 (This is a given constant)
4. 1.12112 (This is a given constant)
5. [tex]\(5 - \sqrt{3} \approx 3.267949192431123\)[/tex]
6. 9.23242 (This is a given constant)
Sixth Row:
1. [tex]\(\frac{4}{3} \approx 1.3333333333333333\)[/tex]
2. [tex]\(4 \sqrt{5} \approx 8.94427190999916\)[/tex]
3. [tex]\(4 \sqrt{4} = 4 \times 2 = 8.0\)[/tex]
4. [tex]\(\sqrt[3]{8} = 2.0\)[/tex]
5. 9 (This is a given constant)
6. [tex]\(\sqrt{5} \approx 2.23606797749979\)[/tex]
Seventh Row:
1. -[tex]\(\frac{2}{4} = -0.5\)[/tex]
2. -[tex]\(\sqrt{9} = -3.0\)[/tex]
3. [tex]\(3 - \frac{3}{4} = 3 - 0.75 = 2.25\)[/tex]
4. [tex]\(6 \sqrt{3} \approx 10.392304845413264\)[/tex]
5. -[tex]\(\frac{25}{37} \approx -0.6756756756756757\)[/tex]
This results in the following table:
[tex]\[ \begin{array}{|c|c|c|c|c|c|} \hline \multicolumn{6}{|c|}{\text{Mathematical Expressions}} \\ \hline \text{Start Here} & -3 & 2.6457513110645907 & 4.25 & 12.0 & 0.3 \\ \hline 0.8660254037844386 & 2.0 & 2.95 & 2.6666666666666665 & 3.141592653589793 & 0.33333 \\ \hline 6.141592653589793 & 2.080083823051904 & 0.12323 & 11.426149773176359 & \text{NaN} & 2.5 \\ \hline 0.0 & -31 & 12.0 & 9 & -1 & -4 \\ \hline 8 & 9.42477796076938 & 9.89012 & 1.12112 & 3.267949192431123 & 9.23242 \\ \hline 1.3333333333333333 & 8.94427190999916 & 8.0 & 2.0 & 9 & 2.23606797749979 \\ \hline -0.5 & -3.0 & 2.25 & 10.392304845413264 & -0.6756756756756757 & \text{End Here} \\ \hline \end{array} \][/tex]
[tex]\[ \begin{array}{|c|c|c|c|c|c|} \hline \multicolumn{6}{|c|}{\text{Mathematical Expressions}} \\ \hline \text{Start Here} & -3 & \sqrt{7} & 4.25 & \sqrt{144} & \frac{3}{10} \\ \hline \frac{\sqrt{3}}{2} & \frac{6}{3} & 2.95 & 2 \frac{2}{3} & \pi & 0.33333 \\ \hline \pi + 3 & \sqrt[3]{9} & 0.12323 & 3 + \sqrt{71} & \frac{2}{0} & \frac{5}{2} \\ \hline \frac{0}{2} & -31 & 3 + \sqrt{81} & 3^2 & 2 - 3 & 0 - 4 \\ \hline 2^3 & 3 \pi & 9.89012 & 1.12112 & 5 - \sqrt{3} & 9.23242 \\ \hline \frac{4}{3} & 4 \sqrt{5} & 4 \sqrt{4} & \sqrt[3]{8} & 9 & \sqrt{5} \\ \hline - \frac{2}{4} & -\sqrt{9} & 3 - \frac{3}{4} & 6 \sqrt{3} & -\frac{25}{37} & \text{End Here} \\ \hline \end{array} \][/tex]
Now, we'll solve these expressions one by one:
First Row:
1. -3 (This is a given constant)
2. [tex]\(\sqrt{7} \approx 2.6457513110645907\)[/tex]
3. 4.25 (This is a given constant)
4. [tex]\(\sqrt{144} = 12.0\)[/tex]
5. [tex]\(\frac{3}{10} = 0.3\)[/tex]
Second Row:
1. [tex]\(\frac{\sqrt{3}}{2} \approx 0.8660254037844386\)[/tex]
2. [tex]\(\frac{6}{3} = 2.0\)[/tex]
3. 2.95 (This is a given constant)
4. [tex]\(2 \frac{2}{3} = 2 + \frac{2}{3} = 2.6666666666666665\)[/tex]
5. [tex]\(\pi \approx 3.141592653589793\)[/tex]
6. 0.33333 (This is a given constant)
Third Row:
1. [tex]\(\pi + 3 \approx 6.141592653589793\)[/tex]
2. [tex]\(\sqrt[3]{9} \approx 2.080083823051904\)[/tex]
3. 0.12323 (This is a given constant)
4. [tex]\(3 + \sqrt{71} \approx 11.426149773176359\)[/tex]
5. [tex]\(\frac{2}{0}\)[/tex] (Division by zero is undefined, so we use NaN which stands for Not a Number)
6. [tex]\(\frac{5}{2} = 2.5\)[/tex]
Fourth Row:
1. [tex]\(\frac{0}{2} = 0.0\)[/tex]
2. -31 (This is a given constant)
3. [tex]\(3 + \sqrt{81} = 3 + 9 = 12.0\)[/tex]
4. [tex]\(3^2 = 9\)[/tex]
5. 2 - 3 = -1
6. 0 - 4 = -4
Fifth Row:
1. [tex]\(2^3 = 8\)[/tex]
2. [tex]\(3 \pi \approx 9.42477796076938\)[/tex]
3. 9.89012 (This is a given constant)
4. 1.12112 (This is a given constant)
5. [tex]\(5 - \sqrt{3} \approx 3.267949192431123\)[/tex]
6. 9.23242 (This is a given constant)
Sixth Row:
1. [tex]\(\frac{4}{3} \approx 1.3333333333333333\)[/tex]
2. [tex]\(4 \sqrt{5} \approx 8.94427190999916\)[/tex]
3. [tex]\(4 \sqrt{4} = 4 \times 2 = 8.0\)[/tex]
4. [tex]\(\sqrt[3]{8} = 2.0\)[/tex]
5. 9 (This is a given constant)
6. [tex]\(\sqrt{5} \approx 2.23606797749979\)[/tex]
Seventh Row:
1. -[tex]\(\frac{2}{4} = -0.5\)[/tex]
2. -[tex]\(\sqrt{9} = -3.0\)[/tex]
3. [tex]\(3 - \frac{3}{4} = 3 - 0.75 = 2.25\)[/tex]
4. [tex]\(6 \sqrt{3} \approx 10.392304845413264\)[/tex]
5. -[tex]\(\frac{25}{37} \approx -0.6756756756756757\)[/tex]
This results in the following table:
[tex]\[ \begin{array}{|c|c|c|c|c|c|} \hline \multicolumn{6}{|c|}{\text{Mathematical Expressions}} \\ \hline \text{Start Here} & -3 & 2.6457513110645907 & 4.25 & 12.0 & 0.3 \\ \hline 0.8660254037844386 & 2.0 & 2.95 & 2.6666666666666665 & 3.141592653589793 & 0.33333 \\ \hline 6.141592653589793 & 2.080083823051904 & 0.12323 & 11.426149773176359 & \text{NaN} & 2.5 \\ \hline 0.0 & -31 & 12.0 & 9 & -1 & -4 \\ \hline 8 & 9.42477796076938 & 9.89012 & 1.12112 & 3.267949192431123 & 9.23242 \\ \hline 1.3333333333333333 & 8.94427190999916 & 8.0 & 2.0 & 9 & 2.23606797749979 \\ \hline -0.5 & -3.0 & 2.25 & 10.392304845413264 & -0.6756756756756757 & \text{End Here} \\ \hline \end{array} \][/tex]
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