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Chapter 1: Q2B. (page 55)

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

A circle with a radius of w鈭�4has a circumference of 2蟺w鈭�4.

Short Answer

Expert verified

"A circle with a radius of w鈭�4 is a hypothesis" and "has a circumference of 2蟺(w鈭�4)"is the conclusion.

Step by step solution

01

Step 1. Given Statement.

A circle with a radius of w鈭�4has a circumference of 2蟺(w鈭�4).

02

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.

03

Step 3. Formula used.

Circumference of a circle with radius r is given by:

2蟺r

04

Step 4. Calculation.

Circumference=2蟺r=2蟺w鈭�4

Thus, if the radius of the circle is w鈭�4, then the circumference is 2蟺(w鈭�4).

Thus, a circle with a radius w鈭�4is a hypothesis and has a circumference of 2蟺(w鈭�4)its conclusion.

05

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鈭�4, then the circumference of a circle is 2蟺(w鈭�4).

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