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x^3y^2 z = 360
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25 Nov 2021, 15:05
25 Nov 2021, 15:05
1
Expert Reply
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Question Stats:
16% (01:45) correct
83% (01:09) wrong based on 12 sessions
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\(x^3y^2 z = 360\). Choose all possible options.
A. x > y > z
B. x < y < z
C. x < y and y > z
D. x > y and y < z
E. None of the above
A. x > y > z
B. x < y < z
C. x < y and y > z
D. x > y and y < z
E. None of the above
ShowHide Answer
Official Answer
A,B,C,D
x^3y^2 z = 360
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04 Dec 2021, 00:25
04 Dec 2021, 00:25
1
Expert Reply
We are given that:
\(x^{3} * y^{2} * z = 360\)
Now multiple cases are possible here:
Case 1:
When \(x = -2\) and \(y = -3\) and \(z = -5\), then:
\(x^{3} * y^{2} * z = (-2) * (-2) * (-2) * (-3) * (-3) * (-5)\)
\(x^{3} * y^{2} * z = (-2)^{3} * (-3)^{2} * (-5)\)
\(x > y > z\)
In this situation, option A) is a possible answer.
Case 2:
When \(x = 2\) and \(y = 3\) and \(z = 5\), then:
\(x^{3} * y^{2} * z = (2) * (2) * (2) * (3) * (3) * (5)\)
\(x^{3} * y^{2} * z = (2)^{3} * (3)^{2} * (5)\)
\(x < y < z\)
So, option B) is a possible answer as well.
Case 3:
When \(x = -2\) and \(y = 3\) and \(z = -5\), then:
\(x^{3} * y^{2} * z = (-2) * (-2) * (-2) * (3) * (3) * (-5)\)
\(x^{3} * y^{2} * z = (-2)^{3} * (3)^{2} * (-5)\)
\(x <y\) and \(y > z\)
In this situation, option C) is a possible answer.
Case 4:
When \(x = 2\) and \(y = -3\) and \(z = 5\), then:
\(x^{3} * y^{2} * z = (2) * (2) * (2) * (-3) * (-3) * (5)\)
\(x^{3} * y^{2} * z = (2)^{3} * (-3)^{2} * (5)\)
\(x > y\) and \(y < z\)
Therefore, option D) is also a possible answer.
Hence, the correct answers are Option A), Option B), Option C), and Option D).
\(x^{3} * y^{2} * z = 360\)
Now multiple cases are possible here:
Case 1:
When \(x = -2\) and \(y = -3\) and \(z = -5\), then:
\(x^{3} * y^{2} * z = (-2) * (-2) * (-2) * (-3) * (-3) * (-5)\)
\(x^{3} * y^{2} * z = (-2)^{3} * (-3)^{2} * (-5)\)
\(x > y > z\)
In this situation, option A) is a possible answer.
Case 2:
When \(x = 2\) and \(y = 3\) and \(z = 5\), then:
\(x^{3} * y^{2} * z = (2) * (2) * (2) * (3) * (3) * (5)\)
\(x^{3} * y^{2} * z = (2)^{3} * (3)^{2} * (5)\)
\(x < y < z\)
So, option B) is a possible answer as well.
Case 3:
When \(x = -2\) and \(y = 3\) and \(z = -5\), then:
\(x^{3} * y^{2} * z = (-2) * (-2) * (-2) * (3) * (3) * (-5)\)
\(x^{3} * y^{2} * z = (-2)^{3} * (3)^{2} * (-5)\)
\(x <y\) and \(y > z\)
In this situation, option C) is a possible answer.
Case 4:
When \(x = 2\) and \(y = -3\) and \(z = 5\), then:
\(x^{3} * y^{2} * z = (2) * (2) * (2) * (-3) * (-3) * (5)\)
\(x^{3} * y^{2} * z = (2)^{3} * (-3)^{2} * (5)\)
\(x > y\) and \(y < z\)
Therefore, option D) is also a possible answer.
Hence, the correct answers are Option A), Option B), Option C), and Option D).
