The Temperature at the Point $( x , y ) \text { on a metal plate is } T = \frac { 9 x } { x ^ { 2 } + y ^ { 2 } } \text {. Find the }$

question 67

Multiple Choice

The temperature at the point $( x , y ) \text { on a metal plate is } T = \frac { 9 x } { x ^ { 2 } + y ^ { 2 } } \text {. Find the }$ direction of greatest increase in heat from the point $( 7,9 )$ . Round all numerical values in your answer to three decimal places.

• A) \(0.101 \hat { \mathbf { i } } - 0.023 \hat { \mathbf { j } }\)
• B) \(0.034 \hat { \mathbf { i } } - 0.017 \hat { \mathbf { j } }\)
• C) \(0.023 \hat { \mathbf { i } } - 0.034 \hat { \mathbf { j } }\)
• D) \(0.038 \hat { \mathbf { i } } - 0.101 \hat { \mathbf { j } }\)
• E) \(0.017 \hat { \mathbf { i } } - 0.067 \hat { \mathbf { j } }\)

---

Definitions:

Simplify

The process of making something less complex or easier to understand, often applied to mathematical expressions or procedures.

Simplify

To reduce something to its most basic or uncomplicated form, making it easier to understand or deal with.

R

Often used as a symbol representing the interest rate or rate of return in financial equations.

Budgeted Sales

The projected amount of sales revenue a company expects to earn over a specific period, often used for planning purposes.