1) Given 2<a<3, 5<b<6 Find:
b
a−b
2) Given 2<a<3, 5<b<6 Find:
a/b
2<a<3, 5<b<6 Find:
b: all we know is that 5<b<6
a-b: the smallest difference is when the largest value is subtracted from the smallest value. So,
2-6 < a-b < 3-5
-4 < a-b < -2
the largest quotient is when the largest value is divided by the smallest value. So,
2<a<3, 5<b<6
2/6 < a/b < 3/5
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To find the values of b and a-b when given the ranges for a and b, we can simply take the average of the minimum and maximum values within their respective ranges.
1) Given 2 < a < 3 and 5 < b < 6:
To find b, we take the average of the minimum and maximum values in the range for b:
b = (5 + 6) / 2 = 5.5
To find a-b, we substitute the average value of b into the equation:
a - b = a - 5.5
Now, since the range for a is 2 < a < 3, we can take any value within that range for a. Let's pick a = 2.5:
a - b = 2.5 - 5.5 = -3
Thus, b = 5.5 and a - b = -3.
2) Given 2 < a < 3 and 5 < b < 6:
To find a/b, we divide the average value of a by the average value of b:
a/b = (2 + 3) / (5 + 6) = 5/11
Therefore, a/b = 5/11.