The boundary weights of this car part are .98 21.5 = 21.07 and 1.02 21.5 = 21.93 grams. The problem states that the piece cannot weigh less than the minimum weight or more than the maximum weight in order for it to work. This means that the part will function at boundary weights themselves, and the lower and upper bounds are included. The answer to the problem is 21.07 ≤ x ≤ 21.93, where x is the weight of the part in grams. Finding the range of a particular variable is essentially an exercise in close reading. Every time you come across a question involving ranges, you should carefully peruse the problem to pick out whether a particular variable’s range includes its bounds or not. This inclusion is the difference between “less than or equal to” and simply “less than.” Operations on Ranges Operations like addition, subtraction, and multiplication can be performed on ranges just like they can be performed on variables. For example:
If 4 < x < 7, what is the range of 2x + 3?
To solve this problem, simply manipulate the range like an inequality until you have a solution. Begin with the original range: Then multiply the inequality by 2: Add 3 to the inequality, and you have the answer: There is one crucial rule you need to know about multiplying ranges: if you multiply a range by a negative number, you must flip the 美国GREater-than or less-than signs. For instance, if you multiply the range 2 < x < 8 by –1, the new range will be –2 > x > –8. Math IC questions that ask you to perform operations on ranges of one variable will often test your alertness by making you multiply the range by a negative number. Some range problems on the Math IC will be made slightly more difficult by the inclusion of more than one variable. In general, the same basic procedures for dealing with one-variable ranges applies to adding, subtracting, and multiplying two-variable ranges. Addition with Ranges of Two or More Variables
If –2 < x < 8 and 0 < y < 5, what is the range of x + y?
Simply add the ranges. The lower bound is –2 + 0 = –2. The upper bound is 8 + 5 = 13. Therefore, –2 < x + y < 13. Subtraction with Ranges of Two or More Variables
Suppose 4 < s < 7 and –3 < t < –1. What is the range of s – t?
In this case, you have to find the range of –t. By multiplying the range of t by –1 and reversing the direction of the inequalities, we find that 1 < –t < 3. Now we can simply add the ranges again to find the range of s – t. 4 + 1 = 5, and 7 + 3 = 10. Therefore, 5 < s – t < 10. In general, to subtract ranges, find the range of the opposite of the variable being subtracted, and then add the ranges as usual. Multiplication with Ranges of Two or More Variables
If –1 < j < 4 and 6 < k < 12, what is the range of jk?英语作文
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