Answer :
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].
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].
