Ask Question
10 March, 23:00

Arrange the reasons for the proof in the correct order. Prove: If the diameter of a circle is 6 meters and the formula for diameter is d = 2r, then the radius of the circle is 3 meters.

+2
Answers (1)
  1. 10 March, 23:34
    0
    Given the question: Arrange the reasons for the proof in the correct order. Prove: If the diameter of a circle is 6 meters and the formula for diameter is d = 2r, then the radius of the circle is 3 meters.

    A. If r ≠ 3 m, then d ≠ 6 m. Since the contrapositive is true, the original statement must also be true. Therefore, if the diameter of a circle is 6 meters, then the radius is 3 meters.

    B. Multiplication of real numbers shows that d = 2 (2 m) = 4 m.

    C. Substitute r = 2 m into d = 2r.

    D. Assume that r ≠ 3 m. For example, the radius equals another length, such as r = 2 m.

    To prove that i f the diameter of a circle is 6 meters and the formula for diameter is d = 2r, then the radius of the circle is 3 meters by contradiction, we assume that the radius in not equal to 3 meters, for example, the radius equals another length, such as r = 2 m.

    Next, we substitute the value: r = 2m nto the original equation that says that d = 2r, i. e. d = 2 (2m) = 4m which is not true and contradicts the original statement that the diameter of the circle is 6m.

    Therefore, the arrangement of the proof is as follows:

    D. Assume that r ≠ 3 m. For example, the radius equals another length, such as r = 2 m.

    C. Substitute r = 2 m into d = 2r.

    B. Multiplication of real numbers shows that d = 2 (2 m) = 4 m.

    A. If r ≠ 3 m, then d ≠ 6 m. Since the contrapositive is true, the original statement must also be true. Therefore, if the diameter of a circle is 6 meters, then the radius is 3 meters.

    D C B A.
Know the Answer?
Not Sure About the Answer?
Get an answer to your question ✅ “Arrange the reasons for the proof in the correct order. Prove: If the diameter of a circle is 6 meters and the formula for diameter is d = ...” in 📙 Mathematics if there is no answer or all answers are wrong, use a search bar and try to find the answer among similar questions.
Search for Other Answers