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If X is between -3 and -1, and Y is between - 1 and 1, then X2 - Y2 is in between which of the following?
- a)-9 and 1
- b)-9 and -1
- c)0 and 8
- d)0 and 9
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
If X is between -3 and -1, and Y is between - 1 and 1, then X2 - Y2 is...
To find the range of values for X² - Y², we need to consider the range of values for X and Y separately, and then calculate the corresponding range for X² - Y².
Range of X:
Given that X is between -3 and -1, we can write this as:
-3 < x="" />< />
Range of Y:
Given that Y is between -1 and 1, we can write this as:
-1 < y="" />< />
Calculating range for X² - Y²:
To determine the range for X² - Y², we substitute the extreme values (lower and upper bounds) of X and Y into the expression X² - Y² and compare the results.
1. Lower bounds:
Substituting -3 for X and -1 for Y, we have:
X² - Y² = (-3)² - (-1)²
= 9 - 1
= 8
2. Upper bounds:
Substituting -1 for X and 1 for Y, we have:
X² - Y² = (-1)² - 1²
= 1 - 1
= 0
Therefore, the range of values for X² - Y² is between 0 and 8.
Hence, the correct answer is option C) 0 and 8.
Range of X:
Given that X is between -3 and -1, we can write this as:
-3 < x="" />< />
Range of Y:
Given that Y is between -1 and 1, we can write this as:
-1 < y="" />< />
Calculating range for X² - Y²:
To determine the range for X² - Y², we substitute the extreme values (lower and upper bounds) of X and Y into the expression X² - Y² and compare the results.
1. Lower bounds:
Substituting -3 for X and -1 for Y, we have:
X² - Y² = (-3)² - (-1)²
= 9 - 1
= 8
2. Upper bounds:
Substituting -1 for X and 1 for Y, we have:
X² - Y² = (-1)² - 1²
= 1 - 1
= 0
Therefore, the range of values for X² - Y² is between 0 and 8.
Hence, the correct answer is option C) 0 and 8.
Community Answer
If X is between -3 and -1, and Y is between - 1 and 1, then X2 - Y2 is...
Answer is c here
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If X is between -3 and -1, and Y is between - 1 and 1, then X2 - Y2 is in between which of the following?a)-9 and 1b)-9 and -1c)0 and 8d)0 and 9Correct answer is option 'C'. Can you explain this answer?
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