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

question 157

Multiple Choice

Solve the problem.
-Write an iterated triple integral in the order $\mathrm { dy } \mathrm {} \mathrm { dz } \mathrm { dx }$ for the volume of the region in the first octant enclosed by the cylinder $x ^ { 2 } + z ^ { 2 } = 49$ and the plane $y = 4$ .

• A) \(\int _ { 0 } ^ { 7 } \int _ { 0 } ^ { \sqrt { 49 - x ^ { 2 } } } \int _ { 0 } ^ { 4 } d y d z d x\)
• B) \(\int _ { 0 } ^ { 7 } \int _ { 0 } ^ { \sqrt { 49 - z ^ { 2 } } } \int _ { 0 } ^ { 4 } d y d z d x\)
• C) \(\int _ { 0 } ^ { 7 } \int _ { 0 } ^ { \sqrt { 49 - z ^ { 2 } } } \int _ { 0 } ^ { 4 - z } d y d z d x\)
• D) \(\int _ { 0 } ^ { 7 } \int _ { 0 } ^ { \sqrt { 49 - x ^ { 2 } } } \int _ { 0 } ^ { z } d y d z d x\)

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Definitions:

Residual Value

The estimated amount that an asset will be worth at the end of its useful life, after deducting any expected costs of disposal.

Straight-Line Method

A method of calculating depreciation by evenly spreading the cost of an asset over its expected useful life.

Depreciation Rate

The percentage rate at which an asset decreases in value over a specific period, often used for tax and accounting purposes.

Residual Value

The estimated amount that an asset will be worth at the end of its useful life.