Question

A rectangular park has an area of 1.36×10 to the power of 8 ft2 . The length of the park is 1.6×10 to the power of 4 ft. Divide the area by the length to find the width of the park.(1 point)
Responses

8.5×10 to the power of 2 ft.
8.5 times 10 squared ft.

8.5×10 to the power of 3 ft.
8.5 times 10 cubed ft.

8.5×10 to the power of 4 ft.
8.5 times 10 superscript 4 baseline ft.

8.5×10 to the power of 5 ft.

Answer 1

To find the width of the park, you can divide the area by the length.

The area of the park is given as:

\[
1.36 \times 10^8 \, \text{ft}^2
\]

The length of the park is:

\[
1.6 \times 10^4 \, \text{ft}
\]

To find the width (\(w\)), you can use the formula:

\[
w = \frac{\text{Area}}{\text{Length}} = \frac{1.36 \times 10^8}{1.6 \times 10^4}
\]

Now perform the division:

1. Divide the coefficients:

\[
\frac{1.36}{1.6} = 0.85
\]

2. Subtract the exponents:

\[
10^{8-4} = 10^4
\]

This gives:

\[
w = 0.85 \times 10^4
\]

To express \(0.85\) in scientific notation, it can be rewritten as:

\[
8.5 \times 10^{-1}
\]

Thus:

\[
w = 8.5 \times 10^{-1} \times 10^{4} = 8.5 \times 10^{3} \, \text{ft}
\]

So the width of the park is:

\[
8.5 \times 10^{3} \, \text{ft}
\]

The correct response is:

**8.5×10 to the power of 3 ft.**