A block of copper at a temperature of $50^{\circ} \mathrm{C}$ is placed in contact with a block of aluminum at a temperature of $45^{\circ} \mathrm{C}$ in an insulated container. As a result of a transfer of 2500 J of energy from the copper to the aluminum, the final equilibrium temperature of the two blocks is $48^{\circ} \mathrm{C}.$ What is the change in the energy of the Universe?

A 50-g block of copper (one mole has a mass of 63.5 g) at a temperature of $35^{\circ} \mathrm{C}$ is put in contact with a 100-g block of aluminum (molar mass 27 g) at a temperature of $20^{\circ} \mathrm{C}.$ The blocks are inside an insulated enclosure, with little contact with the walls. At these temperatures, the high-temperature limit is valid for the specific heat. Calculate the final temperature of the two blocks. Do NOT look up the specific heats of aluminum and copper; you should be able to figure them out on your own.

a. Sketch the graph of $f(x)=x^{2}-\frac{3}{x}$, for $-4 \leq x \leq 4$. b. Write down the equation of the vertical asymptote of f(x). c. On the same diagram draw the graph of $g(x)=-3(2)^{x}+9$, for $-4 \leq x \leq 4$. d. Write down the equation of the horizontal asymptote of g(x). e. Find the coordinates of the points of intersection of f(x) and g(x).

Give an example of a Pythagorean triple that is not a multiple of 3, 4, 5.

Complete the table of particles involved in radioactive decay.

$$\begin{matrix} \text{Particle Name} & \text{Symbol} & \text{Mass Number} & \text{Atomic Number or Charge}\\ \text{alpha particle} & \ {_2 ^4He} & \text{ } & \text{ }\\ \text{ } & \ {^0 _{-1} e} & \text{ } & \text{-1}\\ \text{gamma ray} & \ {^0 _0 Y} & \text{ } & \text{ }\\ \text{positron} & \text{ } & \text{0} & \text{ }\\ \text{ } & \ {^1 _0 n} & \text{1} & \text{ }\\ \text{proton} & \ {^1 _1 p} & \text{ } & \text{ }\\ \end{matrix}$$

Find an expression for the change in entropy when two blocks of the same substance and of equal mass, one at the temperature $T_{h}$ the other at $T_{e},$ are brought into thermal contact and allowed to reach equilibrium. Evaluate the change in entropy for two blocks of copper, each of mass 500 g, with $C_{pm}=24.4\ \mathrm{JK}^{-1}\ \mathrm{mol}^{-1},$ taking $T_{\mathrm{h}}=500 \mathrm{K}$ and $T_{e}=250 \mathrm{K}.$

Find the general solution of the separable differential equation given. Note that this problem, maybe the general solution will be a relationship between x and y, rather than y = f(x).

$$x y \frac{d y}{d x}=\frac{\ln x}{\sqrt{1-y^{2}}}$$

Investigate the given two parameter family of functions. Assume that a and b are positive. (a) Graph f(x) using b = 1 and three different values for a. (b) Graph f(x) using a = 1 and three different values for b. (c) In the graphs in parts (a) and (b), how do the critical points of f appear to move as a increases? As b increases? (d) Find a formula for the x-coordinates of the critical point(s) of f in terms of a and b. $f ( x ) = ( x - a ) ^ { 2 } + b$

Compare the attitude toward the beloved in Petrarch's "Sonnet 292” with that in Shakespeare's “Sonnet 130.” How does each speaker view his beloved?

Según la información de la etiqueta, ¿cuántas calorías tiene una ración de arroz con frijoles negros? ¿Cuántos gramos de proteínas tiene una ración?

The hypotenuse of a $30^{\circ}$ $-60^{\circ}$ $-90^{\circ}$ triangle has a length of 2r. What are the lengths of the other two legs?

What can you say about the determinant of an $n \times n$ matrix with the following form?

$$\left[\begin{array}{ccccc}{0} & {0} & {\cdots} & {0} & {1} \\ {0} & {0} & {\cdots} & {1} & {0} \\ {\vdots} & {\vdots} & {} & {\vdots} & {\vdots} \\ {0} & {1} & {\cdots} & {0} & {0} \\ {1} & {0} & {\cdots} & {0} & {0}\end{array}\right]$$

The maximum production of a soft-drink bottling company is 5000 cartons per day. The company produces two kinds of soft drinks, regular and diet. It costs $1.00 to produce each carton of regular and$1.20 to produce each carton of diet. The daily operating budget is $5400. The profit is$0.15 per carton on regular and $0.17 per carton on diet drinks. How much of each type of drink is produced to obtain the maximum profit?

What is object performance?