The value of `(5.42x5.42+5.42xx24)/(32.71xx32.71-27.29xx27.29)div(6.54xx6.54-3.46xx3.46)/(3.08xx5+3.08xx45)` is equal to

Options

A. 0.3
B. 0.4
C. 0.7
D. 2.5

Answer

To solve the expression \((5.42 \times 5.42 + 5.42 \times 24) / (32.71 \times 32.71 - 27.29 \times 27.29) \div (6.54 \times 6.54 - 3.46 \times 3.46) / (3.08 \times 5 + 3.08 \times 45)\), we can follow these steps:

### Step 1: Simplify the Numerator
The numerator is \(5.42 \times 5.42 + 5.42 \times 24\). We can factor out \(5.42\):

\[ 5.42 \times (5.42 + 24) = 5.42 \times 29.42 \]

### Step 2: Simplify the Denominator
The denominator is \(32.71 \times 32.71 - 27.29 \times 27.29\). This is a difference of squares, which can be factored as:

\[ (32.71 - 27.29)(32.71 + 27.29) \]

Calculating these values:

\[ 32.71 - 27.29 = 5.42 \]
\[ 32.71 + 27.29 = 60 \]

Thus, the denominator simplifies to:

\[ 5.42 \times 60 \]

### Step 3: Combine the Results
Now we can substitute back into the expression:

\[ \frac{5.42 \times 29.42}{5.42 \times 60} \]

The \(5.42\) cancels out:

\[ \frac{29.42}{60} \]

### Step 4: Simplify the Division
Next, we need to evaluate the second part of the expression:

\((6.54 \times 6.54 - 3.46 \times 3.46)\). This is also a difference of squares:

\[ (6.54 - 3.46)(6.54 + 3.46) \]

Calculating these values:

\[ 6.54 - 3.46 = 3.08 \]
\[ 6.54 + 3.46 = 10 \]

Thus, this part simplifies to:

\[ 3.08 \times 10 \]

### Step 5: Evaluate the Last Part
Now, for the last part, \(3.08 \times 5 + 3.08 \times 45\), we can factor out \(3.08\):

\[ 3.08 \times (5 + 45) = 3.08 \times 50 \]

### Step 6: Combine All Parts
Now we can substitute everything back into the expression:

\[ \frac{\frac{29.42}{60}}{3.08 \times 10} \div (3.08 \times 50) \]

This simplifies to:

\[ \frac{29.42}{60 \times (3.08 \times 10) \times (3.08 \times 50)} \]

### Step 7: Final Calculation
Calculating the denominator:

\[ 60 \times 3.08 \times 10 \times 3.08 \times 50 = 60 \times 3.08^2 \times 500 \]

Now, we can compute the final value.

### Final Answer
After performing the calculations, we find the final value of the expression.

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