[tex]\[ a = \frac{b^2 + c}{d} \][/tex]

Find [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]. Write your answer in standard form.

[tex]\[ a = \][/tex]



Answer :

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]