Certainly! Let's work through this step-by-step to find the value of [tex]\( R \)[/tex] and then convert it to standard form.
We are given:
[tex]\[
R = \frac{x^2}{y}
\][/tex]
where:
[tex]\[
x = 3.8 \times 10^5
\][/tex]
[tex]\[
y = 5.9 \times 10^4
\][/tex]
### Step 1: Calculate [tex]\( x^2 \)[/tex]
First, let's calculate [tex]\( x^2 \)[/tex]:
[tex]\[
x^2 = (3.8 \times 10^5)^2
\][/tex]
When squaring, we need to apply the exponent rule [tex]\((a \times 10^b)^2 = a^2 \times 10^{2b}\)[/tex]:
[tex]\[
x^2 = 3.8^2 \times 10^{2 \times 5}
\][/tex]
[tex]\[
3.8^2 = 14.44
\][/tex]
Therefore:
[tex]\[
x^2 = 14.44 \times 10^{10}
\][/tex]
### Step 2: Divide by [tex]\( y \)[/tex]
Now we need to compute:
[tex]\[
R = \frac{14.44 \times 10^{10}}{5.9 \times 10^4}
\][/tex]
We can simplify this division:
[tex]\[
R = \frac{14.44}{5.9} \times 10^{10} \div 10^4
\][/tex]
[tex]\[
R = \frac{14.44}{5.9} \times 10^{10-4}
\][/tex]
[tex]\[
R = \frac{14.44}{5.9} \times 10^6
\][/tex]
### Step 3: Simplify the fraction
Now, evaluate the fraction:
[tex]\[
\frac{14.44}{5.9} \approx 2.447457627118644
\][/tex]
Thus:
[tex]\[
R = 2.447457627118644 \times 10^6
\][/tex]
### Step 4: Convert to standard form
To express [tex]\( R \)[/tex] in standard form, we round the value to three significant figures:
[tex]\[
R \approx 2.447 \times 10^6
\][/tex]
### Final Answer
The value of [tex]\( R \)[/tex] is:
[tex]\[
R \approx 2.447 \times 10^6
\][/tex]
In standard form, to an appropriate degree of accuracy, the result is [tex]\( 2.447 \times 10^6 \)[/tex].
