To find the value of [tex]\( a \)[/tex] when [tex]\( b = 4 \times 10^2 \)[/tex], [tex]\( c = 6 \times 10^3 \)[/tex], and [tex]\( d = 2 \times 10^2 \)[/tex], we need to substitute these values into the given formula:
[tex]\[
a = \frac{b^2 + c}{d}
\][/tex]
Let's break down the calculations step-by-step:
1. First, we calculate [tex]\( b \)[/tex]:
[tex]\[
b = 4 \times 10^2 = 400
\][/tex]
2. Next, we calculate [tex]\( c \)[/tex]:
[tex]\[
c = 6 \times 10^3 = 6000
\][/tex]
3. Now we calculate [tex]\( d \)[/tex]:
[tex]\[
d = 2 \times 10^2 = 200
\][/tex]
4. Then, we need to square [tex]\( b \)[/tex]:
[tex]\[
b^2 = 400^2 = 160000
\][/tex]
5. Add [tex]\( c \)[/tex] to [tex]\( b^2 \)[/tex]:
[tex]\[
b^2 + c = 160000 + 6000 = 166000
\][/tex]
6. Finally, we divide the result by [tex]\( d \)[/tex]:
[tex]\[
a = \frac{166000}{200} = 830.0
\][/tex]
So, the value of [tex]\( a \)[/tex] is:
[tex]\[
a = 830.0
\][/tex]
