Write C in the blank if the sentence is correctly punctuated. _____ It sprinkled on and off at the picnic; nevertheless, we still had a good time.

Graph the function rule. Explain why the graph is continuous or discrete. Your cost c to buy w pounds of walnuts at $6/Ib Is represented by c = 6w.

Show that the Debye model of a d-dimensional crystal predicts that the low temperature heat capacity is proportional to $T^{d}$.

A Carnot engine is coupled to a Carnot refrigerator so that all of the work produced by the engine is used by the refrigerator in extraction of heat from a heat reservoir at $0^\circ C$ at the rate of $35 kJ \cdot s^{−1}.$ The source of energy for the Carnot engine is a heat reservoir at $250^\circ C.$ If both devices discard heat to the surroundings at $25^\circ C,$ how much heat does the engine absorb from its heat-source reservoir? If the actual coefficient of performance of the refrigerator is $\omega=0.6 \omega_{\mathrm{Carnot}}$ and if the thermal efficiency of the engine is $\eta=0.6 \eta_{\mathrm{Carnot},}$ how much heat does the engine absorb from its heat-source reservoir?

Find the radius of convergence of the power series. $\sum_{n=1}^{\infty} \frac{n}{n+1}(-2 x)^{n-1}$

Find the area of the region bounded by the curves $y=\frac{x}{x^{2}-2 x+2}, y=\frac{2}{x^{2}-2 x+2}$, and x=0.

Graph the linear equation. $\frac{1}{3} x+2 y=8$

A two-phase system of liquid water and water vapor in equilibrium at 8000 kPa consists of equal volumes of liquid and vapor. If the total volume $V^{t}=0.15 \mathrm{m}^{3}$ , what is the total enthalpy $H^{t}$ and what is the total entropy $S^{t} ?$

In polar coordinates, $x=r \cos \theta \text { and } y=r \sin \theta$. The definition of x implies that $\frac{\partial x}{\partial r}=\cos \theta=\frac{x}{r}$. But we also have $x^{2}+y^{2}=r^{2}$, so differentiating with respect to r gives $2 x \frac{\partial x}{\partial r}=2 r \quad \Longrightarrow \quad \frac{\partial x}{\partial r}=\frac{r}{x}$. But eqns 11.41 and 11.42 imply that $\frac{\partial x}{\partial r}=\frac{\partial r}{\partial x}$. What’s gone wrong?

How much heat is required when 10,000 kg of $CaCO_3$ is heated at atmospheric pressure from $50^\circ C$ to $880^\circ C?$

Find the arc Length of the following curves on the given interval. y=-8x-3 on [-2, 6] (Use calculus.)

What is the first step in checking for arithmetic errors when two column tota ls are not in balance?

A small business earns a profit of $6500 in January and$17,500 in May. What is the rate of change in profit for this time period? Justify your answer.

Consider the graph of the equation y = mx + b. a. How does changing the value of m affect the graph of the equation? b. How does changing the value of b affect the graph of the equation?