Suppose the temperature at any point $( x , y ) \text { in a steel plate is }$ $T = 500 - 0.6 x ^ { 2 } - 1.5 y ^ { 2 }$ where $x$ and $y$ are measured in meters. At the point $( 8,7 )$ find the rate of change of the temperature with respect to the distance moved along the plate in the direction of the $x$-axis. Round your answer to one decimal place.
A) $- 7.2 ^ { \circ } / \mathrm { m }$
B) $- 9.6 ^ { \circ } / \mathrm { m }$
C) $38.4 ^ { \circ } / \mathrm { m }$
D) $3.4 ^ { \circ } / \mathrm { m }$
E) $- 5.2 ^ { \circ } / \mathrm { m }$

Question

Quizplus · Accepted Answer

To find the rate of change of the temperature $T$ with respect to the distance moved along the $x$-axis, we need to compute the partial derivative of $T$ with respect to $x$, denoted as $\frac{\partial T}{\partial x}$. For $T = 500 - 0.6x^2 - 1.5y^2$, $\frac{\partial T}{\partial x} = -1.2x$. Substituting $x = 8$, we get $\frac{\partial T}{\partial x} = -1.2 \times 8 = -9.6 ^{\circ}/\mathrm{m}$.

Suppose the Temperature at Any Point (x,y) in a steel plate is ( x , y ) \text { in a steel plate is }(x,y) in a steel plate is

Suppose the Temperature at Any Point $( x , y ) \text { in a steel plate is }$