Question

Identify the hypothesis and conclusion of each statement. Then write each statement in if-then form.

A circle with a radius of $w-4$has a circumference of $2\pi \left(w-4\right)$.

Short answer

"A circle with a radius of $w-4$ is a hypothesis" and "has a circumference of $2\pi (w-4)$"is the conclusion.

Step-by-step solution

Step 1. Given Statement.

A circle with a radius of $w-4$has a circumference of $2\pi (w-4)$.

Step 2. Description of step.

To identify the hypotheses and conclusion in the given statement.

As the radius of the circle is given, use it to find the circumference.

Step 3. Formula used.

Circumference of a circle with radius r is given by:

$2\pi r$

Step 4. Calculation.

$\begin{array}{l}\text{Circumference}=2\pi r\\ =2\pi \left(w-4\right)\end{array}$

Thus, if the radius of the circle is $w-4$, then the circumference is $2\pi (w-4)$.

Thus, a circle with a radius $w-4$is a hypothesis and has a circumference of $2\pi (w-4)$its conclusion.

Step 5. Write in if-then form.

To write the given statement in if-then form, use the word if before the hypothesis and use the word then before the conclusion. So, we have

If the circle has a radius $w-4$, then the circumference of a circle is $2\pi (w-4)$.