What is the value of `((3pi^c)/(4)+(11pi^c)/(5)+(7pi^c)/(10))` , when converted to degrees?

Options

A. `135^(@)`
B. `245^(@)`
C. `657^(@)`
D. `810^(@)`

Answer

To solve the problem, we need to evaluate the expression \(\frac{3\pi}{4} + \frac{11\pi}{5} + \frac{7\pi}{10}\) and convert the result from radians to degrees.

### Step-by-step Solution:

1. **Identify the expression**:
We have the expression:
\[ \frac{3\pi}{4} + \frac{11\pi}{5} + \frac{7\pi}{10} \]

2. **Find a common denominator**:
The denominators are 4, 5, and 10. The least common multiple (LCM) of these numbers is 20.

3. **Convert each term to have the common denominator**:
- For \(\frac{3\pi}{4}\):
\[ \frac{3\pi}{4} = \frac{3\pi \cdot 5}{4 \cdot 5} = \frac{15\pi}{20} \]
- For \(\frac{11\pi}{5}\):
\[ \frac{11\pi}{5} = \frac{11\pi \cdot 4}{5 \cdot 4} = \frac{44\pi}{20} \]
- For \(\frac{7\pi}{10}\):
\[ \frac{7\pi}{10} = \frac{7\pi \cdot 2}{10 \cdot 2} = \frac{14\pi}{20} \]

4. **Combine the fractions**:
Now, we can add the fractions:
\[ \frac{15\pi}{20} + \frac{44\pi}{20} + \frac{14\pi}{20} = \frac{(15 + 44 + 14)\pi}{20} = \frac{73\pi}{20} \]

5. **Convert to degrees**:
We know that \(\pi\) radians is equal to 180 degrees. Therefore, we convert \(\frac{73\pi}{20}\) radians to degrees:
\[ \frac{73\pi}{20} \times \frac{180}{\pi} = \frac{73 \times 180}{20} \]

6. **Calculate the final value**:
Simplifying the expression:
\[ \frac{73 \times 180}{20} = \frac{13140}{20} = 657 \]

Thus, the value of the expression when converted to degrees is **657 degrees**.