Find the Center of Mass of a Thin Plate Covering $x$

question 245

Multiple Choice

Find the center of mass of a thin plate covering the given region with the given density function.
-The region between the $x$ -axis and the curve $y = \frac { 2 } { x ^ { 2 } } , 1 \leq x \leq 2$ , with density $\delta ( x ) = \frac { x ^ { 2 } } { 2 }$

• A) \(\bar { x } = \frac { 3 } { 2 } , \bar { y } = \frac { 1 } { 2 }\)
• B) \(\bar { x } = \frac { 3 } { 2 } , \bar { y } = 1\)
• C) \(\bar { x } = \frac { 3 } { 2 } , \bar { y } = \frac { 3 } { 2 }\)
• D) \(\bar { x } = \frac { 5 } { 4 } , \bar { y } = \frac { 1 } { 2 }\)

---

Definitions:

Cash Dividends

are payments made by a corporation to its shareholders from profits in the form of cash, reflecting a portion of the corporate earnings being distributed.

Note Payable

A financial obligation or a loan that is documented through a formal agreement stating repayment terms.

Noncash Financing

Financing activities that do not involve cash flows, but rather the exchange of non-cash items or liabilities, such as issuing stock for assets or converting debt to equity.

Amortization of Patents

The gradual write-off of the cost of a patent over its useful life to reflect its consumption, expiration, or decline in value.