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# There are several ways to write Newton's Law of Heating and Cooling. If an object is at temperature $H$ in an environment at temperature $T_{\text {ens }}$ then one form of the law is: $\frac{d H}{d t}=k\left(T_{e n v}-H\right)$ If the environment is hotter than the object, determine the sign of $\frac{d H}{d t}$ and $T_{e n v}-H$. Both are negative Both are positive Both depend on the sign of $\mathrm{k}$ There are several ways to write Newton's Law of Heating and Cooling. If an object is at temperature $H$ in an environment at temperature $T_{e n s}$ then one form of the law is: $\frac{d H}{d t}=k\left(T_{e n v}-H\right)$ If the environment is cooler than the object, determine the sign of $\frac{d H}{d t}$ and $T_{\text {env }}-H$. Both are positive Both depend on the sign of $\mathrm{k}$ Both are negative There are several ways to write Newton's Law of Heating and Cooling. If an object is at temperature $H$ in an environment at temperature $T_{e n v}$ then one form of the law is: $\frac{d H}{d t}=k\left(T_{e n v}-H\right)$ In this formula, which of the following statement is true? $\mathrm{k}$ must be positive $k$ must be negative The sign of $\mathrm{k}$ depends on whether the object is heating up or cooling down. For the differential equation $\frac{d Q}{d t}=5(Q-2)$ which of the following is true? $Q(t)$ will be increasing for all time if $Q(0)=0$. $Q(t)$ will be decreasing for all time if $Q(0)=3$. $Q(t)$ will be neither increasing nor decreasing over time if $Q(0)=2$. $Q(t)$ will be increasing if $\mathrm{t}>2$  