The value of `((2.8)^(3)+(2.2)^(3))/((28)^(2)-28xx22+484` is:

Options

A. `0.02`
B. `0.05`
C. `0.01`
D. `0.5`

Answer

To solve the given expression \(\frac{(2.8)^3 + (2.2)^3}{(28)^2 - 28 \times 22 + 484}\), we will follow these steps:

### Step 1: Calculate the numerator
The numerator is \((2.8)^3 + (2.2)^3\).

Using the formula for the sum of cubes, \(a^3 + b^3 = (a + b)(a^2 - ab + b^2)\), where \(a = 2.8\) and \(b = 2.2\):

1. Calculate \(a + b\):
\[ 2.8 + 2.2 = 5.0 \]

2. Calculate \(a^2\):
\[ (2.8)^2 = 7.84 \]

3. Calculate \(b^2\):
\[ (2.2)^2 = 4.84 \]

4. Calculate \(ab\):
\[ 2.8 \times 2.2 = 6.16 \]

5. Now substitute into the formula:
\[ a^2 - ab + b^2 = 7.84 - 6.16 + 4.84 = 6.52 \]

6. Therefore, the numerator becomes:
\[ (2.8)^3 + (2.2)^3 = (5.0)(6.52) = 32.6 \]

### Step 2: Calculate the denominator
The denominator is \((28)^2 - 28 \times 22 + 484\).

1. Calculate \((28)^2\):
\[ (28)^2 = 784 \]

2. Calculate \(28 \times 22\):
\[ 28 \times 22 = 616 \]

3. Now substitute into the denominator:
\[ 784 - 616 + 484 = 784 - 616 + 484 = 652 \]

### Step 3: Combine the results
Now we can combine the results from the numerator and denominator:
\[ \frac{32.6}{652} \]

### Step 4: Simplify the fraction
To simplify \(\frac{32.6}{652}\):
1. Divide both the numerator and denominator by 32.6:
\[ \frac{32.6 \div 32.6}{652 \div 32.6} = \frac{1}{20} \]

2. Convert \(\frac{1}{20}\) to decimal:
\[ \frac{1}{20} = 0.05 \]

### Final Answer
The value of the expression is \(0.05\).

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