The value of `((0.013)^3 + (0.007)(0.000049))/((0.007)^2 + 0.013(0.013-0.007))` is ............

Options

A. 0.06
B. 0.02
C. 0.07
D. 0.04

Answer

To solve the expression \(\frac{(0.013)^3 + (0.007)(0.000049)}{(0.007)^2 + 0.013(0.013-0.007)}\), we will break it down step by step.

### Step 1: Calculate the numerator
The numerator is given by:
\[ (0.013)^3 + (0.007)(0.000049) \]

Calculating \((0.013)^3\):
\[ (0.013)^3 = 0.000002197 \]

Calculating \((0.007)(0.000049)\):
\[ (0.007)(0.000049) = 0.000000343 \]

Now, adding these two results together:
\[ 0.000002197 + 0.000000343 = 0.00000254 \]

### Step 2: Calculate the denominator
The denominator is given by:
\[ (0.007)^2 + 0.013(0.013-0.007) \]

Calculating \((0.007)^2\):
\[ (0.007)^2 = 0.000049 \]

Calculating \(0.013(0.013-0.007)\):
\[ 0.013(0.013 - 0.007) = 0.013(0.006) = 0.000078 \]

Now, adding these two results together:
\[ 0.000049 + 0.000078 = 0.000127 \]

### Step 3: Combine the results
Now we can combine the results from the numerator and the denominator:
\[ \frac{0.00000254}{0.000127} \]

### Step 4: Perform the division
Calculating the division:
\[ \frac{0.00000254}{0.000127} \approx 0.020 \]

### Final Answer
The value of the expression is approximately \(0.020\).

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