Refer to the figure and use the principle of superposition to Find the component of the current $i$ through $R_{3}$ that is due to $V_{S 2}$.

$$\begin{aligned} & V_{S 1}=V_{S 2}=450 \mathrm{~V} \\ & R_{1}=7 \Omega \quad R_{2}=5 \Omega \\ & R_{3}=10 \Omega \quad R_{4}=R_{5}=1 \Omega \end{aligned}$$

Why is the following situation impossible? An air rifle is used to shoot 1.00-g particles at a speed of vx = 100 m/s. The rifle’s barrel has a diameter of 2.00 mm. The rifle is mounted on a perfectly rigid support so that it is fired in exactly the same way each time. Because of the uncertainty principle, however, after many firings, the diameter of the spray of pellets on a paper target is 1.00 cm.

Underline any verbs that are used incorrectly. In the space provided, write the correct form (or $C$ if correct) and the number of the $\mathrm{G} / \mathrm{M}$ principle illustrated. When you finish, compare your responses with those provided at the bottom of this page. If your responses differ, study carefully the principles in parentheses.

Everyone except the temporary workers employed during the past year has become eligible for health benefits.

Applying Le Chatelier's principle, in which direction will the equilibrium shift, (if at all)?

$$\mathrm{CH}_4(\mathrm{~g})+2 \mathrm{~O}_2(\mathrm{~g}) \rightleftharpoons \mathrm{CO}_2(\mathrm{~g})+2 \mathrm{~H}_2 \mathrm{O}(\mathrm{g})+802.3 \mathrm{~kJ}$$

(a) if the temperature is increased
(b) if a catalyst is added
(c) if $\mathrm{CH}_4$ is added
(d) if the volume of the reaction vessel is decreased

Solve each minimum problem using the duality principle. Minimize

$$C = x_1 +2x_2 +x_3$$

subject to the constraints 2

$$\left\{ \begin{array}{rcl} x_1 & -3x_2 & +4x_3 \geq 12 \\ 3x_1 & +x_2 & +2x_3 \geq 10 \\ x_1 & -x_2 & -x_3 \geq -8 \\ x_1 \geq 0, & x_2 \geq 0, & x_3 \geq 0 \end{array} \right.$$

Underline any verbs that are used incorrectly. In the space provided, write the correct form (or $C$ if correct) and the number of the $\mathrm{G} / \mathrm{M}$ principle illustrated. When you finish, compare your responses with those provided at the bottom of this page. If your responses differ, study carefully the principles in parentheses.

Are you convinced that Google's database of customers' messages and private information are secure?

A rocket sled with a mass of 2900 kg moves at 250 m/s on a set of rails. At a certain point, a scoop on the sled dips into a trough of water located between the tracks and scoops water into an empty tank on the sled. By applying the principle of conservation of linear momentum, determine the speed of the sled after 920 kg of water has been scooped up. Ignore any retarding force on the scoop.

Photodissociation of water

$$\mathrm{H}_2 \mathrm{O}(l)+h v \longrightarrow \mathrm{H}_2(g)+\frac{1}{2} \mathrm{O}_2(g)$$

has been suggested as a source of hydrogen. The energy for the reaction is $285.8 \mathrm{~kJ}$ per mole of water decomposed. Calculate the maximum wavelength (in $\mathrm{nm}$ ) that would provide the necessary energy. In principle, is it feasible to use sunlight as a source of energy for this process?

In a population of rabbits, f (C$_{1}$) = $0.70$ and f (C$_{2}$) = $0.30$. The alleles exhibit an incomplete dominance relationship in which C$_{1}$C$_{1}$ produces black rabbits, C$_{1}$C$_{2}$ tan-colored rabbits, and C$_{2}$C$_{2}$ rabbits with white fur. If the assumptions of the Hardy-Weinberg principle apply to the rabbit population, what are the expected frequencies of black, tan, and white rabbits?

Underline any verbs that are used incorrectly. In the space provided, write the correct form (or $C$ if correct) and the number of the $\mathrm{G} / \mathrm{M}$ principle illustrated. When you finish, compare your responses with those provided at the bottom of this page. If your responses differ, study carefully the principles in parentheses.

Google's data team have been carefully studying how to shield users from unwarranted government intrusion.

Show how a single block of glass can be used to turn a p-polarized beam of light through $180^{\circ},$ with the light suffering (in principle) zero reflective loss. The light is incident from air, and the returning beam (also in air) may be displaced sideways from the incident beam. Specify all pertinent angles and use n = 1.45 for glass. More than one design is possible here.

use Archimedes’ Principle, which states that when a sphere of radius r with density

$$d_s$$

is placed in a liquid of density

$$d_L=62.5lb/ft^3$$

,it will sink to a depth h where .

$$\dfrac{π}{3}(3rh^2-h^3)d_L=\dfrac{4}{3}πr^3d_s$$

Find an approximate value for h if:

$$r=5 ft$$

and

$$d_s=20lb/ft^3$$

Use the counting principle to determine the answer to part (a). Assume that each event is equally likely to occur. Two coins are tossed. (a) Determine the number of sample points in the sample space. (b) Construct a tree diagram and list the sample space. Determine the probability that (c) No tails are tossed. (d) Exactly one tail is tossed. (e) Two tails are tossed. (f) At least one tail is tossed.

Show that, in principle, $\mathrm{Na}_2 \mathrm{CO}_3(\mathrm{aq})$ can be converted almost completely to $\mathrm{NaOH}(\mathrm{aq})$ by the reaction

$$\begin{aligned} \mathrm{Ca}(\mathrm{OH})_2(\mathrm{~s})+\mathrm{Na}_2 \mathrm{CO}_3(\mathrm{aq}) & \longrightarrow \\ & \mathrm{CaCO}_3(\mathrm{~s})+2 \mathrm{NaOH}(\mathrm{aq}) \end{aligned}$$