Question
A rocket ship is travelling at an average speed of 1.75 × 104 miles per hour. How many miles will the rocket ship travel in 1.2 × 102 hours?
1. Write the expression: (1.75 × 104)(1.2 × 102)
2. Rearrange the expression: (1.75 × 1.2)(104 × 102)
3. Multiply the coefficients: (2.1)(104 × 102)
4. Apply the product of powers: 2.1 × 10y
The rocket ship will travel 2.1 × 10y miles. What is the value of y in the solution?
y =
1. Write the expression: (1.75 × 104)(1.2 × 102)
2. Rearrange the expression: (1.75 × 1.2)(104 × 102)
3. Multiply the coefficients: (2.1)(104 × 102)
4. Apply the product of powers: 2.1 × 10y
The rocket ship will travel 2.1 × 10y miles. What is the value of y in the solution?
y =
Answers
GPT-4o mini
To solve for the value of \( y \) in the expression \( 2.1 \times 10^y \), we need to evaluate the powers of 10 from the rearranged expression given above.
You have the expression:
\[
(1.75 \times 10^4)(1.2 \times 10^2)
\]
After rearranging, we have:
\[
(1.75 \times 1.2)(10^4 \times 10^2)
\]
Calculating the coefficients:
\[
1.75 \times 1.2 = 2.1
\]
For the powers of 10, we can use the product of powers property:
\[
10^4 \times 10^2 = 10^{4 + 2} = 10^6
\]
Now, we put these together:
\[
2.1 \times 10^6
\]
In the final expression \( 2.1 \times 10^y \), we can see that \( y = 6 \).
Thus, the value of \( y \) is:
\[
\boxed{6}
\]
You have the expression:
\[
(1.75 \times 10^4)(1.2 \times 10^2)
\]
After rearranging, we have:
\[
(1.75 \times 1.2)(10^4 \times 10^2)
\]
Calculating the coefficients:
\[
1.75 \times 1.2 = 2.1
\]
For the powers of 10, we can use the product of powers property:
\[
10^4 \times 10^2 = 10^{4 + 2} = 10^6
\]
Now, we put these together:
\[
2.1 \times 10^6
\]
In the final expression \( 2.1 \times 10^y \), we can see that \( y = 6 \).
Thus, the value of \( y \) is:
\[
\boxed{6}
\]