The first and second laws of thermodynamics are sometimes stated as “You can’t win” and “You can’t even break even.” Do these sayings accurately characterize the laws of thermodynamics as applied to heat engines? Why or why not?

A ball of mass m is connected to two rubber bands of length L, each under tension T. The ball is displaced by a small distance y perpendicular to the length of the rubber bands. Assuming the tension does not change, show that (a) the restoring force is -(2T/L)y and (b) the system exhibits simple harmonic motion with an angular frequency $\omega=\sqrt{2} T / m L$.

The relationship between f and g is given. Explain the relationship between $f^{\prime}$ and $g^{\prime}$. g(x)=3f(x)-1

Match each equation in Column I with a description of its graph from Column lI as it relates to the graph of $y=x^2$.

$$\begin{matrix} \text{I} & \text{II}\\ \text{(a) }{ y=(x-7)^{2}} & \text{A. a translation 7 units to the left}\\ \text{ (b) }{ y=x^{2}-7} & \text{B. a translation 7 units to the right}\\ \text{ (c) }{ y=7 x^{2}} & \text{C. a translation 7 units up}\\ \text{ (d) }{ y=(x+7)^{2}} & \text{D. a translation 7 units down}\\ \text{(e) }{ y=x^{2}+7 } & \text{E. a vertical stretching by a factor of 7}\\ \end{matrix}$$

It gets pretty hot in your apartment. In browsing the Internet, you ind a company selling small “room air conditioners.” You place the air conditioner on the loor, plug it in, and—the advertisement says—it will lower the room temperature up to . Should you $10^{\circ} \mathrm{F}$. Should you order one? Explain.

It gets pretty hot in your apartment. In browsing the Internet, you find a company selling small “room air conditioners.” You place the air conditioner on the floor, plug it in, and—the advertisement says—it will lower the room temperature up to $10^{\circ} \mathrm{F}$. Should you order one? Explain.

For each polynomial function find the following: (A) Degree of the polynomial. (B) All x intercepts. (C) The y intercept. $f(x)=x^{3}(x+5)$

Lok Co. reports net sales of $5,856,480 for 2016 and$8,679,690 for 2017. End-of-year balances for total assets are 2015, $1,686,000; 2016,$1,800,000; and 2017, $1,982,000. (a) Compute Lok’s total asset turnover for 2016 and 2017. (b) Comment on Lok’s efficiency in using its assets if its competitors average a total asset turnover of 3.0.

Write an equation for each ellipse. foci at (0, -3), (0, 3); the point (8, 3) on ellipse

Suppose two worlds, each having mass M and radius R, coalesce int o a single world. Due to gravitational contraction, the combined world has a radius of only $\frac{3}{4} R$. What is the average density of the combined world as a multiple of $\boldsymbol{\rho}_{0}$, the average density of the original two worlds?

Based on your work so far, if you know the area of three squares, you can tell if they will connect at their corners to form a right triangle. But what if you know that a triangle has a right angle? Will the lengths of the sides be related in this way? Work with your team to look more closely at side lengths of some right triangles. a. On centimeter graph paper, form a right angle by drawing one 5-cm length and one 12-cm length as shown at right. If you do not have centimeter graph paper, then use any graph paper to draw and measure these lengths with a ruler. After drawing the two lengths, create a right triangle by connecting the ends of the two lengths with a third side. b. With a ruler, measure the longest side of the triangle in centimeters and label this length. If you do not have a centimeter ruler or you are using another kind of graph paper, create your triangle using 5 and 7 grid units. Then use an edge of the page and the grid lines as your ruler. c . Visualize a square connected to each side of the right triangle in part (b). On your paper, sketch a picture like the one at right. What is the area of each square? Is the area of the square that is connected to the longest side equal to the sum of the areas of the other two squares? d. Check this pattern with a new example. • Draw a new right angle on the centimeter paper like you did in part (a) . This time, use 9-cm and 12-cm lengths. • Connect the endpoints to create a triangle , and measure the third side. • Create a sketch for this triangle like the one you created in part ( c), and find the areas of the squares. Is the area of the square that is connected to the longest side equal to the sum of the other two areas? e. The two shortest sides of a right triangle are called the legs, and the longest side is called the hypotenuse. You previously wrote a statement about the relationship between the areas of squares drawn on the sides of a right triangle. Now use words to describe the relationship between the lengths of the legs and the length of the hypotenuse.

A student performing a double-slit experiment is using a green laser with a wavelength of 530 nm. She is confused when the m = 5 maximum does not appear. She had predicted that this bright fringe would be 1.6 cm from the central maximum on a screen 1.5 m behind the slits. a. Explain what prevented the fifth maximum from being observed. b. What is the width of her slits?

(A) Find the linear and quadratic functions that best fit the data points (0,1.3), (1,0.6), (2,1.5), (3,3.6) and (4,7.4). Round coefficients to two decimal places. (B) Which of the two functions best fits the data? Explain.

Mary needs to row her boat across a 100-m-wide river that is flowing to the east at a speed of 1.0 m/s. Mary can row with a speed of 2.0 m/s. a. If Mary points her boat due north, how far from her intended landing spot will she be when she reaches the opposite shore? b. What is her speed with respect to the shore?