Solve the Problem $\mathrm { dz } \mathrm { dy } \mathrm {} \mathrm { dx }$

question 322

Multiple Choice

Solve the problem.
-Write an iterated triple integral in the order $\mathrm { dz } \mathrm { dy } \mathrm {} \mathrm { dx }$ for the volume of the tetrahedron cut from the first octant by the plane $\frac { x } { 10 } + \frac { y } { 3 } + \frac { z } { 5 } = 1$ .

• A) \(\int _ { 0 } ^ { 10 } \int _ { 0 } ^ { 1 - y / 3 } \int _ { 0 } ^ { 1 - x / 10 - y / 3 } d z d y d x\)
• B) \(\int _ { 0 } ^ { 10 } \int _ { 0 } ^ { 1 - x / 10 } \int _ { 0 } ^ { 1 - x / 10 - y / 3 } d z d y d x\)
• C)\(\int_{0}^{10} \int_{0}^{3(1-x / 10)} \int_{0}^{5(1-x / 10-y / 3)} d z d y d x\)
• D)\(\int_{0}^{10} \int_{0}^{10(1-y / 3)} \int_{0}^{5(1-x / 10-y / 3)} d z d y d x\)

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Definitions:

Emotional Trauma

A psychological condition resulting from an extremely distressing experience, leading to lasting emotional pain and mental disturbance.

Posttraumatic Stress Disorder

A psychiatric disorder that can occur in people who have experienced or witnessed a traumatic event, characterized by flashbacks, nightmares, severe anxiety, and uncontrollable thoughts about the event.

Dark Triad

A psychological term referring to the personality traits of narcissism, Machiavellianism, and psychopathy, which are typically associated with a callous-manipulative interpersonal style.

Malicious Traits

Characteristics or qualities of an individual that are harmful, cruel, or ill-intentioned.