The temperature at the point $( x , y ) \text { on a metal plate is modeled by }$ $T ( x , y ) = 300 e ^ { - \left( x ^ { 2 } + y \right) / 2 } , x \geq 0 , y \geq 0$. Find the directions of no change in heat on the plate from the point $( 5,7 )$.
A) There will be no change in directions perpendicular to the gradient $\pm ( 15 \mathbf { i } - \mathbf { j } )$.
B) There will be no change in directions parallel to the gradient $\pm ( 10 \mathbf { i } - \mathbf { j } )$.
C) There will be no change in directions parallel to the gradient $\pm ( \mathbf { i } + 10 \mathbf { j } )$.
D) There will be no change in directions perpendicular to the gradient $\pm ( \mathbf { i } + 15 \mathbf { j } )$.
E) There will be no change in directions perpendicular to the gradient $\pm ( \mathbf { i } - 10 \mathbf { j } )$.

Question

Quizplus · Accepted Answer

The Answer of The temperature at the point $( x , y ) \text { on a metal plate is modeled by }$ $T ( x , y ) = 300 e ^ { - \left( x ^ { 2 } + y \right) / 2 } , x \geq 0 , y \geq 0$. Find the directions of no change in heat on the plate from the point $( 5,7 )$.
A) There will be no change in directions perpendicular to the gradient $\pm ( 15 \mathbf { i } - \mathbf { j } )$.
B) There will be no change in directions parallel to the gradient $\pm ( 10 \mathbf { i } - \mathbf { j } )$.
C) There will be no change in directions parallel to the gradient $\pm ( \mathbf { i } + 10 \mathbf { j } )$.
D) There will be no change in directions perpendicular to the gradient $\pm ( \mathbf { i } + 15 \mathbf { j } )$.
E) There will be no change in directions perpendicular to the gradient $\pm ( \mathbf { i } - 10 \mathbf { j } )$.

The Temperature at the Point (x,y) on a metal plate is modeled by ( x , y ) \text { on a metal plate is modeled by }(x,y) on a metal plate is modeled by

The Temperature at the Point $( x , y ) \text { on a metal plate is modeled by }$