ME The expression $$ \pi(r-3)^{2} $$ represents the area covered by the hour hand a clock in one rotation, where $$ r $$ is the radius of the entire clock. Write a olynomial that represents the area covered by the hour hand in one rotation.

Question

UpStudy AI · Accepted Answer

To express the area covered by the hour hand of a clock in one rotation as a polynomial, let's start with the given expression:

$$
\text{Area} = \pi (r - 3)^2
$$

Here, $$ r $$ is the radius of the entire clock, and $$ \pi (r - 3)^2 $$ represents the area of a circle with radius $$ r - 3 $$.

To convert this into a polynomial, we'll expand the binomial $$(r - 3)^2$$:

$$
(r - 3)^2 = r^2 - 6r + 9
$$

Now, multiply each term by $$ \pi $$ to get the area:

$$
\text{Area} = \pi (r^2 - 6r + 9)
$$

Distributing $$ \pi $$ across the terms gives:

$$
\text{Area} = \pi r^2 - 6\pi r + 9\pi
$$

**Polynomial Representation:**

$$
\text{Area}(r) = \pi r^2 - 6\pi r + 9\pi
$$

This polynomial accurately represents the area covered by the hour hand of the clock in one full rotation.

**Final Answer:**

After expanding, the polynomial is π r² minus six π r plus nine π. Thus,

Area(r) = π r² − 6πr + 9π
The area covered by the hour hand in one rotation is represented by the polynomial: $$ \text{Area}(r) = \pi r^2 - 6\pi r + 9\pi $$

ME The expression represents the area covered by the hour hand
a clock in one rotation, where is the radius of the entire clock. Write a
olynomial that represents the area covered by the hour hand in one rotation.

Solución de inteligencia artificial de Upstudy

Responder

Solución

Mind Expander

preguntas relacionadas

Latest Pre Algebra Questions

ME The expression represents the area covered by the hour hand a clock in one rotation, where is the radius of the entire clock. Write a olynomial that represents the area covered by the hour hand in one rotation.