rectangular park has an area of 1.36×108 ft2 . The length of the park is 1.6×104 ft. Divide the area by the length to find the width of the park.(1 point) Responses 8.5×105 ft. 8.5 times 10 superscript 5 baseline ft. 8.5×102 ft. 8.5 times 10 squared ft. 8.5×104 ft. 8.5 times 10 superscript 4 baseline ft. 8.5×103 ft.

Question

GPT-4o mini · Answer

To find the width of the park, we can use the formula for the area of a rectangle, which is:

\[ \text{Area} = \text{Length} \times \text{Width} \]

Given:

Area = \( 1.36 \times 10^8 \) ft²
Length = \( 1.6 \times 10^4 \) ft

We can find the width by rearranging the formula:

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

Now, let's perform the calculation:

First, we can divide the coefficients:

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

Next, we divide the powers of 10:

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

Putting it all together, we have:

\[ \text{Width} = 0.85 \times 10^4 \]

To express this in scientific notation, \( 0.85 \) can be rewritten as \( 8.5 \times 10^{-1} \). Thus:

\[ \text{Width} = 8.5 \times 10^{-1} \times 10^4 = 8.5 \times 10^{4-1} = 8.5 \times 10^3 \]

So, the width of the park is:

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

The correct response is:

8.5×103 ft.