QuestionSuppose that $6<x<7$ and $10<y<12$ . Find all possible values of each expression. $x y$ $\square<x y<\square$

Studdy Solution

STEP 1

1. We are given the ranges for $x$ and $y$ as $6 < x < 7$ and $10 < y < 12$ , respectively.
2. The product $xy$ will depend on the extreme values within the ranges of $x$ and $y$ .
3. We need to find the minimum and maximum possible values of $xy$ .

STEP 2

1. Determine the minimum possible value of $xy$ .
2. Determine the maximum possible value of $xy$ .

STEP 3

To determine the minimum possible value of $xy$ , we use the lower bounds of $x$ and $y$ .
The minimum value occurs when $x$ is at its lowest value (close to 6) and $y$ is at its lowest value (close to 10).
$\text{Minimum value of } xy \approx 6 \times 10 = 60$

STEP 4

To determine the maximum possible value of $xy$ , we use the upper bounds of $x$ and $y$ .
The maximum value occurs when $x$ is at its highest value (close to 7) and $y$ is at its highest value (close to 12).
$\text{Maximum value of } xy \approx 7 \times 12 = 84$

STEP 5

Combining the results from Steps 1 and 2, the possible range for $xy$ is:
$60 < xy < 84$
Solution: $60 < xy < 84$

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