Provide an Appropriate Response $\mathrm { T } ( \mathrm { x } , \mathrm { y } ) = 25 \mathrm { x } ^ { 2 } - 2 \mathrm { xy } + 9 \mathrm { y } ^ { 2 }$

question 48

Multiple Choice

Provide an appropriate response.
-Let $\mathrm { T } ( \mathrm { x } , \mathrm { y } ) = 25 \mathrm { x } ^ { 2 } - 2 \mathrm { xy } + 9 \mathrm { y } ^ { 2 }$ be the temperature at the point $( \mathrm { x } , \mathrm { y } )$ on the ellipse $\mathrm { x } = 3 \cos \mathrm { t } , \mathrm { y } = 5$ sin $t$ , $0 \leq t \leq 2 \pi$ . Find the minimum and maximum temperatures, $\mathrm { T } _ { \mathrm { min } }$ and $\mathrm { T } _ { \mathrm { max } }$ , respectively, on the ellipse.

• A) \(\mathrm { T } _ { \min } = 210 ; \mathrm { T } _ { \max } = 240\)
• B) \(\mathrm { T } _ { \min } = 435 ; \mathrm { T } _ { \max } = 465\)
• C) \(\mathrm { T } _ { \min } = 0 ; \mathrm { T } _ { \max } = 30\)
• D) \(\mathrm { T } _ { \min } = \frac { \pi } { 4 } ; \mathrm { T } _ { \max } = \frac { 3 \pi } { 4 }\)

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