To evaluate the expression [tex]\( -2\pi + \sqrt{16} \)[/tex], let's break it down step-by-step:
1. Calculate [tex]\( 2\pi \)[/tex]:
The value of [tex]\( \pi \)[/tex] is approximately 3.14159. So:
[tex]\[
2\pi \approx 2 \times 3.14159 = 6.28318
\][/tex]
2. Take the negative of [tex]\( 2\pi \)[/tex]:
[tex]\[
-2\pi \approx -6.28318
\][/tex]
3. Calculate [tex]\( \sqrt{16} \)[/tex]:
The square root of 16 is:
[tex]\[
\sqrt{16} = 4
\][/tex]
4. Combine the two results:
[tex]\[
-2\pi + \sqrt{16} \approx -6.28318 + 4 = -2.28318
\][/tex]
So, the value of the expression [tex]\( -2\pi + \sqrt{16} \)[/tex] is approximately [tex]\(-2.28318\)[/tex].
Now, let's compare this value to the given choices:
- [tex]\(a) -9.8\)[/tex]
- [tex]\(b) -1.8\)[/tex]
- [tex]\(c) 9.8\)[/tex]
- [tex]\(d) -4.5\)[/tex]
Among the choices, the one closest to [tex]\(-2.28318\)[/tex] is:
[tex]\[ -1.8 \][/tex]
Therefore, the closest choice to the calculated value is [tex]\( b) -1.8 \)[/tex].
