Question

What is the circumference of a circle with a diameter of 4.5 miles? Estimate the circumference to the hundredths place using 3.14 for π
.(1 point)
Responses

7.07 miles
7.07 miles

14.13 miles
14.13 miles

14.2 miles
14.2 miles

63.59 miles

Answer 1

Rewrite the irrational cube root 189−−−√3
as the product of an integer and another irrational cube root. Show your work.

Answer 2

To find the circumference of a circle, you can use the formula:

\[
C = \pi \times d
\]

where \( C \) is the circumference and \( d \) is the diameter. Given that the diameter is 4.5 miles and using \( \pi \approx 3.14 \), we can calculate:

\[
C = 3.14 \times 4.5
\]

Now, let's do the multiplication:

\[
C = 3.14 \times 4.5 = 14.13 \text{ miles}
\]

So, the estimated circumference of the circle, rounded to the hundredths place, is **14.13 miles**.

Answer 3

To rewrite the expression \( \sqrt[3]{189} \) as the product of an integer and another irrational cube root, we can first factor the number 189.

1. **Factor 189:**
\[
189 = 3^3 \times 7
\]
Here, we can see that \( 189 \) can be factored into \( 27 \times 7 \), where \( 27 \) is \( 3^3 \).

2. **Rewrite the cube root:**
\[
\sqrt[3]{189} = \sqrt[3]{27 \times 7}
\]

3. **Use the property of cube roots:**
The cube root of a product can be expressed as the product of the cube roots:
\[
\sqrt[3]{27 \times 7} = \sqrt[3]{27} \times \sqrt[3]{7}
\]

4. **Calculate the cube root of 27:**
Since \( 27 = 3^3 \), we have:
\[
\sqrt[3]{27} = 3
\]

5. **Combine the results:**
Now we can put it all together:
\[
\sqrt[3]{189} = 3 \times \sqrt[3]{7}
\]

Thus, the expression \( \sqrt[3]{189} \) can be rewritten as the product of an integer and another irrational cube root:

\[
\sqrt[3]{189} = 3 \sqrt[3]{7}
\]