An RC series circuit consists of an AC source, a $33.0 - \mu \text F$ capacitor, and a 30.0-$\Omega$ resistor. If the source emf is given by $\varepsilon = \varepsilon_ { max } \sin ( \omega t )$, where $E _ { \max } = 180.0 \mathrm { V }$ and $\omega = 20.0 \mathrm { s } ^ { - 1 }$, what is the current amplitude?

Riley and Rhoda plan to buy several bags of dog food and a dog collar. Each bags of dog food costs $7, and the dog collar costs$5. a. Use the information above to write an expression for the amount of money they will spend if they buy b bags of food. b. Riley and Rhoda have $30. Use this information and the expression you wrote for Part (a) to write an inequality for finding the number of bags of food they could buy. c. Solve the inequality and graph the solutions. Check your answer in the original situation.

Find the distance from $(-1,7)$ to the line $x=3$.

Write the correct word in the space next to each definition.

random $\rule{2cm}{0.15mm}$

Write a program that prompts the user to enter the radius and draws four circles in the center of the screen.

Find the exponential decay equation for a population that halves in size every unit of time and that has 1024 individuals at time 0.

Write a program that prompts the user to enter the center of a rectangle, width, and height, and displays the rectangle.

The table shows the time it took several members of a cycling club to bike different distances. Sort the cyclists from least to greatest unit rate.

A child's hoop of mass M and radius b rolls in a straight line with velocity v. Its top is given a light tap with a stick at right angles to the direction of motion. The impulse of the blow is $I.$ a. Show that this results in a deflection of the line of rolling by angle $\phi=I / M v,$ assuming that the gyroscope approximation holds and neglecting friction with the ground. b. Show that the gyroscope approximation is valid provided $F \ll M v^{2} / b,$ where F is the peak applied force.

Given a 1-, 3-, and 4-$\mu$F capacitor, can they be interconnected to obtain an equivalent 2-$\mu$F capacitor?

Integrative: Determining relevant cash flows Lombard Company is contemplating the purchase of a new high-speed widget grinder to replace the existing grinder. The existing grinder was purchased 2 years ago at an installed cost of $60,000; it was being depreciated under MACRS using a 5 -year recovery period. The existing grinder is expected to have a usable life of 5 more years. The new grinder costs$ 105,000 and requires $5,000 in installation costs; it has a 5-year usable life and would be depreciated under MACRS using a 5 -year recovery period. Lombard can currently sell the existing grinder for$ 70,000 without incurring any removal or cleanup costs. To support the increased business resulting from purchase of the new grinder, accounts receivable would increase by $40,000, inventories by$ 30,000, and accounts payable by $58,000. At the end of 5 years, the existing grinder would have a market value of zero; the new grinder would be sold to net$ 29,000 after removal and cleanup costs and before taxes. The firm is subject to a 40% tax rate. The estimated earnings before depreciation, interest, and taxes over the 5 years for both the new and the existing grinder are shown in the following table.

b. Determine the incremental operating cash flows associated with the proposed grinder replacement. (Note: Be sure to consider the depreciation in year 6.)

Find the least squares regression line for the points $\{(1, 1), (2, 0), (5, −5) \}$. Graph the points and the line.

Work each of the following. Find the coordinates of all points whose distance from (1, 0) is $\sqrt{10}$ and whose distance from (5, 4) is $\sqrt{10}$.

Let X={a, b, c}. Define a function S from $\mathcal{P}$(X) to the set of bit strings of length 3 as follows. Let Y$\subseteq$X. If a$\in$Y, set $s_1=0$; If a$\notin$Y, set $s_1=1$; If b$\in$Y, set $s_2=0$; If b$\notin$Y, set $s_2=1$; If c$\in$Y, set $s_3=0$; If c$\in$Y, set $s_3=1$. Define S(Y)=$s_1s_2s_3$.

Prove that S is onto.