Mathematics, Part 2
Question 1: State the equation of an ellipse and the information about the ellipse that can be derived from that equation.
Answer 1: The equation of an ellipse is:where a, b, h, and k are constants. From this formula, it can be ascertained that:The center of the ellipse is (h,k).The length of the horizontal axis is 2a. The length of the vertical axis is 2b. If a , the major axis is horizontal and the minor axis is vertical; if b , the major axis is vertical and the minor axis is horizontal.
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Question 2: Explain how to determine the number of significant digits in a measurement. Give an example.
Answer 2: The number of significant digits of a measurement is the number of digits known precisely plus one digit that is estimated. For example, suppose an object is measured with a ruler in which the centimeter is the smallest unit. When measured, the end of the object falls between two centimeter lines, lines 23 and 24. It is estimated that it falls closer to 24 than to 23, but only slightly, so an estimated length of 23.6 is determined for the object. The measurement consists of two precisely known digits, 2 and 3, plus one digit that is estimated, 6. Therefore, the number of significant digits is 3.
Question 3: Explain the term significant digits and its relation to precision.
Answer 3: The number of significant digits, or significant figures, in a number refers to the number of digits that remain after the number has been converted to scientific notation. For example, the number 7300 converts to 7.3 x 103 in scientific notation. It has two significant digits, 7 and 3, after the zeros have been dropped. The more significant digits a number has, the more precise the measurement is.
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