To find [tex]\( R \)[/tex] given the formulas and values:
[tex]\[ R = \frac{x^2}{y} \][/tex]
[tex]\[ x = 3.8 \times 10^5 \][/tex]
[tex]\[ y = 5.9 \times 10^4 \][/tex]
First, let's substitute the given values of [tex]\( x \)[/tex] and [tex]\( y \)[/tex] into the formula:
[tex]\[ R = \frac{(3.8 \times 10^5)^2}{5.9 \times 10^4} \][/tex]
Next, calculate [tex]\( (3.8 \times 10^5)^2 \)[/tex]:
[tex]\[ (3.8 \times 10^5)^2 = 3.8^2 \times (10^5)^2 \][/tex]
[tex]\[ 3.8^2 = 14.44 \][/tex]
[tex]\[ (10^5)^2 = 10^{10} \][/tex]
Therefore,
[tex]\[ (3.8 \times 10^5)^2 = 14.44 \times 10^{10} \][/tex]
Now, substitute this back into our expression for [tex]\( R \)[/tex]:
[tex]\[ R = \frac{14.44 \times 10^{10}}{5.9 \times 10^4} \][/tex]
To simplify this, divide the coefficients and the powers of 10 separately:
[tex]\[ \frac{14.44}{5.9} \approx 2.447457627118644 \][/tex]
[tex]\[ \frac{10^{10}}{10^4} = 10^{6} \][/tex]
Combining these results, we get:
[tex]\[ R = 2.447457627118644 \times 10^6 \][/tex]
Thus, the value of [tex]\( R \)[/tex] is:
[tex]\[ R \approx 2.447 \times 10^6 \][/tex]
This is [tex]\( 2.447 \)[/tex] multiplied by [tex]\( 10^6 \)[/tex], presented in standard form.
