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

Question

.(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

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 2

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

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:

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