The value of `((3.2)^(3) - 0.008)/((3.2)^(2) + 0.64 + 0.04)` is

Options

A. 0
B. 2.994
C. 3.208
D. 3

Answer

To solve the expression \(\frac{(3.2)^3 - 0.008}{(3.2)^2 + 0.64 + 0.04}\), we can follow these steps:

### Step 1: Calculate \((3.2)^3\)
\[ (3.2)^3 = 3.2 \times 3.2 \times 3.2 \]
Calculating \(3.2 \times 3.2\):
\[ 3.2 \times 3.2 = 10.24 \]
Now, multiplying \(10.24\) by \(3.2\):
\[ 10.24 \times 3.2 = 32.768 \]
So, \((3.2)^3 = 32.768\).

### Step 2: Calculate the numerator
Now we can calculate the numerator:
\[ (3.2)^3 - 0.008 = 32.768 - 0.008 = 32.76 \]

### Step 3: Calculate \((3.2)^2\)
\[ (3.2)^2 = 3.2 \times 3.2 = 10.24 \]

### Step 4: Calculate the denominator
Now we can calculate the denominator:
\[ (3.2)^2 + 0.64 + 0.04 = 10.24 + 0.64 + 0.04 \]
Calculating this step by step:
\[ 10.24 + 0.64 = 10.88 \]
\[ 10.88 + 0.04 = 10.92 \]
So, the denominator is \(10.92\).

### Step 5: Calculate the final value
Now we can substitute the values we calculated into the expression:
\[ \frac{32.76}{10.92} \]
Calculating this division:
\[ 32.76 \div 10.92 \approx 3 \]

Thus, the value of the expression is approximately \(3\).

### Final Answer
The value of \(\frac{(3.2)^3 - 0.008}{(3.2)^2 + 0.64 + 0.04}\) is \(3\).

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