Sure, let's solve the problem step by step.
1. Given Values:
- [tex]\( a = 0.6 \)[/tex]
- [tex]\( b = \frac{7}{4} \)[/tex]
- [tex]\( c = \frac{2}{7} \)[/tex]
2. Calculate [tex]\( b^{-1} \)[/tex]:
- The reciprocal of [tex]\(\frac{7}{4}\)[/tex] is calculated as:
[tex]\[
\left(\frac{7}{4}\right)^{-1} = \frac{4}{7}
\][/tex]
- Converting [tex]\(\frac{4}{7}\)[/tex] to decimal form:
[tex]\[
\frac{4}{7} \approx 0.5714285714285714
\][/tex]
3. Calculate [tex]\( c^2 \)[/tex]:
- Squaring [tex]\(\frac{2}{7}\)[/tex]:
[tex]\[
\left(\frac{2}{7}\right)^2 = \frac{2^2}{7^2} = \frac{4}{49}
\][/tex]
- Converting [tex]\(\frac{4}{49}\)[/tex] to decimal form:
[tex]\[
\frac{4}{49} \approx 0.08163265306122448
\][/tex]
4. Calculate the Final Expression:
- We need to evaluate [tex]\(0.6 \times \left(\frac{4}{7}\right) \div \left(\frac{4}{49}\right)\)[/tex]:
[tex]\[
0.6 \times 0.5714285714285714 \div 0.08163265306122448
\][/tex]
5. Multiplying and Dividing:
- First, multiply [tex]\(0.6\)[/tex] by [tex]\(0.5714285714285714\)[/tex]:
[tex]\[
0.6 \times 0.5714285714285714 = 0.34285714285714286
\][/tex]
- Now, divide the result by [tex]\(0.08163265306122448\)[/tex]:
[tex]\[
0.34285714285714286 \div 0.08163265306122448 \approx 4.199999999999999
\][/tex]
So, the final result is:
[tex]\[
0.6 \times \left(\frac{7}{4}\right)^{-1} \div \left(\frac{2}{7}\right)^2 \approx 4.200
\][/tex]
