Verite the set using the descriptive method. —~ “ The set (a, 0, g. 5, ¢} f: the set of the letters in the name |

A capacitor is connected to an AC generator. As the generator’s frequency is increased, the current in the capacitor
A. Increases.
B. Decreases.
C. Does not change.

An experiment was conducted to study the extrusion process of biodegradable packaging foam.

Among the factors considered for their effect on the unit density (mg/ml) were the die temperature (145$\degree$C versus 155$\degree$C) and the die diameter (3 mm versus 4 mm). The results were stored in PackagingFoam3 . Develop a multiple regression model that uses die temperature and die diameter to predict the unit density (mg>ml). Be sure to perform a thorough residual analysis. Do you think that you need to use both independent variables in the model? Explain.

Find the distance between $(-3,7)$ and $(4,-2)$.

For the regression equation obtained in Exercise $15.91$, analyze the residuals by (d) plotting the residuals versus the order in which they were observed.

Ten years ago, Jacobson Recovery purchased a wrecker for $285,000 to move disabled 18-wheelers. He anticipated a salvage value of$50,000 after 10 years. During this time his average annual revenue totaled $52,000. (a) Did he recover his investment and a 12% per year return? (b) If the annual M&O cost was$10,000 the first year and increased by a constant $1000 per year, was the AW positive or negative at 12% per year? Assume the$50,000 salvage was realized.

Find the distance from (-6, 4) to the line y = x.

A DVD drive is mounted on a chassis and is modeled as a single-degree-of-freedom spring, mass, and damper. During normal operation, the drive (having a mass of 0.4 kg) is subject to a harmonic force of 1 N at 10 rad/s. Because of material considerations and static deflection, the stiffness is fixed at 500 N/m and the natural damping in the system is 10 kg/s. The DVD player starts and stops during its normal operation providing initial conditions to the module of $x_0 = 0.001 m$ and $v_0 = 0.5 m/s.$ The DVD drive must not have an amplitude of vibration larger then 0.008 m even during the transient stage. First, compute the response by numerical simulation to see if the constraint is satisfied. If the constraint is not satisfied, find the smallest value of damping that will keep the deflection less than 0.008 m.

Use a proper word to complete each of the following blanks: When the speed of rotation of a shaft equals one of the natural frequencies of the shaft, it is called ______ speed.

Initial investment at various sale prices Edwards Manufacturing Company (EMC) is considering replacing one machine with another. The old machine was purchased 3 years ago for an installed cost of $10,000. The firm is depreciating the machine under MACRS, using a 5-year recovery period. The new machine costs$24,000 and requires $2,000 in installation costs. The firm is subject to a 40% tax rate. In each of the following cases, calculate the initial investment for the replacement. a. EMC sells the old machine for$11,000.

Let $M$ be the module $R^{n}$ described in Example 3 and let $I_{1}, I_{2}, \ldots, I_{n}$ be left ideals of $R .$ Prove that the following are submodules of $M :$ (a) $\left\{\left(x_{1}, x_{2}, \ldots, x_{n}\right) | x_{i} \in I_{i}\right\}$ (b) $\left\{\left(x_{1}, x_{2}, \ldots, x_{n}\right) | x_{i} \in R \text{ and }x_{1}+x_{2}+\cdots+x_{n}=0\right\}$

Use graphing to find the point of intersection of the two lines. Use the earlier example as a guide. $4 x+3 y=18$ and $x-2 y=10$

In the single-source shortest-paths problem, we want to find the shortest-path weights from a source vertex s to all vertices v ∈ V. Given a graph G, write a linear program for which the solution has the property that

$$d_v$$

is the shortest-path weight from s to v for each vertex v ∈ V.

Let $R$ be an integral domain, let $M$ be an $R$ -module and let $N$ be a submodule of $M .$ Suppose $M$ has rank $n, N$ has rank $r$ and the quotient $M / N$ has rank $s .$ Prove that $n=r+s .$ [Let $x_{1}, x_{2}, \ldots, x_{s}$ be elements of $M$ whose images in $M / N$ are a maximal set of independent elements and let $x_{s+1}, x_{s+2}, \ldots, x_{s+r}$ be a maximal set of independent elements in $N .$ Prove that $x_{1}, x_{2}, \ldots, x_{s+r}$ are linependent in $M$ and that for any element $y \in M$ there is a nonzero element $r \in R$ such that $r y$ is a linear combination of these elements. Then use Exercise $2 . ]$