a. A certain element has a phasor voltage of $\mathrm{V} = 100 \angle{30^\circ} \mathrm{V}$ and current of $\mathrm{I} = 5 \angle{120^\circ} \mathrm{A}$. The angular frequency is $1000 \ \mathrm{rad/s}$. Determine the nature and value of the element. b. Repeat for $\mathrm{V} = 20 \angle{-45^\circ} \mathrm{V}$ and current of $\mathrm{I} = 2 \angle{-135^\circ} \mathrm{A}$. c. Repeat for $\mathrm{V} = 50 \angle{45^\circ} \mathrm{V}$ and current of $\mathrm{I} = 10 \angle{45^\circ} \mathrm{A}$.

David wants to solve for x in the equation 4(x+3)=20. He said, "i can rewrite this equation by distributing the 4 on the left side." After distributing, what should his new equation be? Solve this equation using David's method.

True or False. If the average rate of change of a linear function is $\frac{2}{3}$, then if y increases by 3, x will increase by 2.

A voltage $v_C(t) =10 \cos (2000 \pi \mathrm{t})$ is applied to a $10-\mu \mathrm{F}$ capacitance. Find the complex impedance of the capacitance. Find the phasor voltage and current, and construct a phasor diagram. Write the current as a function of time. Sketch the voltage and current to scale versus time. State the phase relationship between the current and voltage.

Evaluate each expression for the given value of x. 2x+3 for x=3 _

The impedance Z, in ohms, of a circuit element is defined as the ratio of the phasor voltage V, in volts, across the element to the phasor current I, in amperes, through the elements. That is $Z=\frac{V}{I}.$ If the voltage across a circuit element is 18 + i volts and the current through the element is 3 - 4i amperes, determine the impedance.

Identify the class width, class midpoints, and class boundaries for the given frequency distribution.

$$\begin{matrix} \text{Weights (Ib) of Discarded Plastic} & \text{Frequency}\\ \text{0.00-0.99} & \text{8}\\ \text{1.00-1.99} & \text{12}\\ \text{2.00-2.99} & \text{6}\\ \text{300-3.99} & \text{0}\\ \text{4.00-4.99} & \text{0}\\ \text{5.00-5.99} & \text{0}\\ \text{6.00-6.99} & \text{0}\\ \text{7.00-7.99} & \text{5}\\ \text{8.00-8.99} & \text{15}\\ \text{9.00-9.99} & \text{20}\\ \end{matrix}$$

Zinc oxide is amphoteric. Write balanced chemical equations for its reactions with an aqueous solution of hydrochloric acid and with an aqueous solution of sodium hydroxide . (Note: The hydroxide complex ion of zinc is [Zn(OH) 4]^2-.)

Suppose that $v_1(t) =100 \cos (\omega \mathrm{t})$ and $v_2(t) = 100 \sin (\omega \mathrm{t})$ Use phasors to reduce the sum $v_s(t) = v_1(t) + v_2(t)$ to a single term of the form $V_m \cos (\omega \mathrm{t}+\theta).$ Draw a phasor diagram, showing $V_1, V_2$ and $V_s$ State the phase relationships between each pair of these phasors.

Graph the equation. Tell whether the equation is a function. y = 1

Choose the letter of the best answer. Cool, clear weather usually follows a a. warm front. b. cold front. c. stationary front. d. occluded front.

A square parking lot of width w is bounded on all sides by a curb of height d with only one opening of width b. During a heavy rain the lot fills with water and it is of interest to determine the time, t, it takes for the water to completely drain from the lot after the rain stops. A scale model is to be used to study this problem, and it is assumed that

$$t=f(w, b, d, g, \mu, \rho)$$

where g is the acceleration of gravity, $\mu$ is the fluid viscosity, and $\rho$ is the fluid density. (a) A dimensional analysis indicates that two important dimensionless parameters are b/w and d/w. What additional dimensionless parameters are required? (b) For a geometrically similar model having a length scale of 1/10, what is the relationship between the drain time for the model and the corresponding drain time for the actual parking lot? Assume all similarity requirements are satisfied. Can water be used as the model fluid? Explain and justify your answer.

A voltage is given by $v(t) =10 \sin \left(1000 \pi t+30^{\circ}\right)$ First, use a cosine function to express v(t). Then, find the angular frequency, the frequency in hertz, the phase angle, the period, and the rms value. Find the power that this voltage delivers to a $50-\Omega$ resistance. Find the first value of time after t = 0 that v(t) reaches its peak value. Sketch v(t) to scale versus time.

Find the Fourier integral representation of the given function.

$$f(x)=\left\{\begin{array}{ll}{0,} & {x<0} \\ {e^{-x},} & {x>0}\end{array}\right.$$