Two carts move in the same direction along a frictionless air track, each acted on by the same constant force for a time interval $\Delta t$. Cart 2 has twice the mass of cart 1. Which one of the following statements is true? Cart 1 has the greater change in momentum.

Chico Company allows its customers to return merchandise within 30 days of purchase. At December 31, 2017, the end of its first year of operations, Chico estimates future-period merchandise returns of $60,000 (cost of$22,500) related to its 2017 sales. On January 3, 2018, a customer returns merchandise with a selling price of $2,000 for a cash refund; the returned merchandise cost$750 and is returned to inventory as it is not defective. a. Prepare the December 31, 2017, year-end adjusting journal entry for estimated future sales returns and allowances (revenue side). b. Prepare the December 31, 2017, year-end adjusting journal entry for estimated future inventory returns and allowances (cost side). c. Prepare the January 3, 2018, journal entry(ies) to record the merchandise returned.

Commercial electricity is generated and transmitted as three-phase electricity. Instead of a single emf $\mathcal{E}=\mathcal{E}_{0} \cos \omega t$, three separate wires carry currents for the emfs $\mathcal{E}_{1}=\mathcal{E}_{0} \cos \omega t, \mathcal{E}_{2}=\mathcal{E}_{0} \cos \left(\omega t+120^{\circ}\right), \text { and } \mathcal{E}_{3}=\mathcal{E}_{0} \cos \left(\omega t-120^{\circ}\right)$. This is why the long-distance transmission lines you see in the countryside have three parallel wires, as do many distribution lines within a city. a. Draw a phasor diagram showing phasors for all three phases of a three-phase emf. b. Show that the sum of the three phases is zero, producing what is referred to as neutral. In single-phase electricity, provided by the familiar 120 V/60 Hz electric outlets in your home, one side of the outlet is neutral, as established at a nearby electrical substation. The other, cal led the hot side, is one of the three phases. (The round opening is connected to ground.) c. Show that the potential difference between any two of the phases has the rms value $\sqrt{3} \mathcal{E}_{\mathrm{rms}}$, where $\mathcal{E}_{\mathrm{rms}}$ is the familiar single-phase rms voltage. Evaluate this potential difference for $\mathcal{E}_{\mathrm{rms}}=120 \mathrm{V}$. Some high-power home appliances, especially electric clothes dryers and hot-water heaters, are designed to operate between two of the phases rather than between one phase and neutral. Heavy-duty industrial motors a re designed to operate from all three phases, but full three-phase power is rare in residential or office use.

Find $f^{\prime}(x)$ in two ways: ( 1 ) using the product or quotient rule and ( 2 ) simplifying first. $f(x)=\frac{x^{4}+4}{x^{4}}$

Revenue. The marketing research department for a company that manufactures and sells notebook computers established the following price-demand and revenue functions: $$ \begin{matrix} \text{p(x)=2,000-60 x} & \text{Price-demand function}\\ \text{R(x) &=x p(x) =x(2,000-60 x)} & \text{Revenue function}\\ \end{matrix} $$ where p(x) is the wholesale price in dollars at which x thousand computers can be sold, and R(x) is in thousands of dollars. Both functions have domain $1 \leq x \leq 25$ (A) Sketch a graph of the revenue function in a rectangular coordinate system. (B) Find the value of x that will produce the maximum revenue. What is the maximum revenue to the nearest thousand dollars? (C) What is the wholesale price per computer (to the nearest dollar) that produces the maximum revenue?

Calculate the y-component of the vector with magnitude 24.0 m and direction $56.0^{\circ}$.

You are told the column totals in a trial balance are not equal. After careful analysis, you discover only one error. Specifically, a correctly journalized credit purchase of an automobile for $18,950 is posted from the journal to the ledger with an$18,950 debit to Automobiles and another $18,950 debit to Accounts Payable. The Automobiles account has a debit balance of$37,100 on the trial balance. (1) Answer each of the following questions and (2) compute the dollar amount of any misstatement for parts a through d. a. Is the Debit column total of the trial balance overstated, understated, or correctly stated? b. Is the Credit column total of the trial balance overstated, understated, or correctly stated? c. Is the Automobiles account balance overstated, understated, or correctly stated in the trial balance? d. Is the Accounts Payable account balance overstated, understated, or correctly stated in the trial balance? e. If the Debit column total of the trial balance is $200,000 before correcting the error, what is the total of the Credit column before correction?

A Texas chemical company had to file for bankruptcy because of a nationwide phaseout of methyl tertiary butyl ether (MTBE). The company is in the planning phase of reorganizing and expects to invest $50 million in a new ethanol production facility. Determine the revenue necessary each month to recover its investment in 3 years, plus interest at a rate of 2% per month, compounded continuously. Solve by (a) formula, and (b) spreadsheet function.

The distance an object travels as a function of time is given by $f(t)=\frac{1}{2} a t^{2}+v_{0} t+x_{0}$, where a is the acceleration, $v_0$ is the initial velocity, and $x_0$ is the initial position of the object. Describe the transformations of the parent functin f(t)=$t^2$ used to graph f(t) for each of the following. $a=2, v_{0}=0, x_{0}=10$

Use point-by-point plotting to sketch the graph of each equation. xy=-6

The period t, in seconds, of the swing of a pendulum is given by the formula $t=2 \pi \sqrt{\frac{L}{32}}$, where L is the length of the pendulum in feet. Find the period of a pendulum 3.5 ft long. Use a calculator, and round the answer to the nearest tenth.

The rate law for the reaction

$$2 \mathrm{NO}(g)+\mathrm{Cl}_2(g) \longrightarrow 2 \mathrm{NOCl}(g)$$

is given by rate $=k[\mathrm{NO}]\left[\mathrm{Cl}_2\right]$. (a) What is the order of the reaction? (b) A mechanism involving the following steps has been proposed for the reaction:

$$\begin{gathered} \mathrm{NO}(g)+\mathrm{Cl}_2(g) \longrightarrow \mathrm{NOCl}_2(g) \\ \mathrm{NOCl}_2(g)+\mathrm{NO}(g)+\mathrm{NO}(g) \longrightarrow 2 \mathrm{NOCl}(g) \end{gathered}$$

If this mechanism is correct, what does it imply about the relative rates of these two steps ?

The rate law for the reaction

$$2 \mathrm{NO}(g)+\mathrm{Cl}_2(g) \longrightarrow 2 \mathrm{NOCl}(g)$$

is given by rate $=k[\mathrm{NO}]\left[\mathrm{Cl}_2\right]$.

(a) What is the order of the reaction?

(b) A mechanism involving the following steps has been proposed for the reaction

$$\begin{gathered} \mathrm{NO}(g)+\mathrm{Cl}_2(g) \longrightarrow \mathrm{NOCl}_2(g) \\ \mathrm{NOCl}_2(g)+\mathrm{NO}(g)+\mathrm{NO}(g) \longrightarrow 2 \mathrm{NOCl}(g) \end{gathered}$$

If this mechanism is correct, what does it imply about the relative rates of these two steps?

The rate law for the reaction

$$2 \mathrm{NO}(g)+\mathrm{Cl}_2(g) \longrightarrow 2 \mathrm{NOCl}(g)$$

is given by rate $=k[\mathrm{NO}]\left[\mathrm{Cl}_2\right]$. (a) What is the order of the reaction? (b) A mechanism involving these steps has been proposed for the reaction

$$\begin{aligned} \mathrm{NO}(g)+\mathrm{Cl}_2(g) &\longrightarrow \mathrm{NOCl}_2(g) \\ \mathrm{NOCl}_2(g)+\mathrm{NO}(g) & \longrightarrow 2 \mathrm{NOCl}(g) \end{aligned}$$

If this mechanism is correct, what does it imply about the relative rates of these two steps?