`(5.75 xx 5.75 xx 5.75 + 3.25 xx 3.25 xx 3.25 )/(57.5 xx 57.5 + 32.5 xx 32.5 - 57.5 xx 32.5)` is equal to :

Options

A. 0.0009
B. 0.009
C. 0.9
D. 0.09

Answer

To solve the expression \((5.75 \times 5.75 \times 5.75 + 3.25 \times 3.25 \times 3.25) / (57.5 \times 57.5 + 32.5 \times 32.5 - 57.5 \times 32.5)\), we can follow these steps:

### Step 1: Calculate the numerator
The numerator consists of two parts:
1. \(5.75 \times 5.75 \times 5.75\)
2. \(3.25 \times 3.25 \times 3.25\)

Calculating each part:
- \(5.75 \times 5.75 = 33.0625\)
- \(5.75 \times 33.0625 = 189.922875\) (This is \(5.75^3\))

- \(3.25 \times 3.25 = 10.5625\)
- \(3.25 \times 10.5625 = 34.328125\) (This is \(3.25^3\))

Now, add these two results together:
\[ 189.922875 + 34.328125 = 224.251 \]

### Step 2: Calculate the denominator
The denominator consists of:
1. \(57.5 \times 57.5\)
2. \(32.5 \times 32.5\)
3. \(57.5 \times 32.5\)

Calculating each part:
- \(57.5 \times 57.5 = 3306.25\)
- \(32.5 \times 32.5 = 1056.25\)
- \(57.5 \times 32.5 = 1868.75\)

Now, substitute these values into the denominator:
\[ 3306.25 + 1056.25 - 1868.75 = 3493.75 \]

### Step 3: Combine the results
Now we can combine the results from the numerator and the denominator:
\[ \frac{224.251}{3493.75} \]

### Step 4: Calculate the final result
Using a calculator or performing the division:
\[ \frac{224.251}{3493.75} \approx 0.0642 \]

Thus, the final answer is approximately \(0.0642\).

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