Solve the area of the shaded region.

Compute the response of a spring–mass system modeled by equation $m \ddot{x}(t)+k x(t)=F_{0} \cos \omega t$ to a force of magnitude 23 N, driving frequency of twice the natural frequency, and initial conditions given by $x_0 = 0 m$ and $v_0= 0.2 m/s.$ The mass of the system is 10 kg, the spring stiffness is 1000 N/m, and the mass of the spring is considered and known to be 1 kg. What percent does the natural frequency change if the mass of the spring is not taken into consideration?

What are the wavelength ranges in (a) the AM radio band $(540-1600 \mathrm{kHz})$, and (b) the FM radio band (88.0$108 \mathrm{MHz}$ )?

In a poll conducted by the Pew Research Center in a certain year, 2000 adults ages 18 years old and older were asked how frequently they are in touch with their parents by phone. The results of the poll are as follows:

If a person who participated in the poll is selected at random, what is the probability that the person said he or she kept in touch with his or her parents:

a. Once a week?

b. At least once a week?

Which element has three electrons in its 3d sublevel?

Carry out the indicated calculation. (3 – 4i)(6 + 2i)

The region between the curve $y=1 /(2 \sqrt{x})$ and the x-axis from x = 1/4 to x = 4 is revolved about the x-axis to generate a solid.

Find the volume of the solid.

Two mass-spring systems with the same mass are undergoing oscillatory motion with the same amplitudes. System 1 has twice the frequency of system 2. How do

(a) their energies

(b) their maximum accelerations compare?

The solid circular shaft and the hollow tube shown in given figure are both attached to a rigid circular plate at their left ends. A torque $T_A=2\ \mathrm{kN} \cdot \mathrm{m}$ applied to the right end of the shaft is resisted by a torque $T_B$ at the right end of the tube. The shaft is made of steel ( $G=$ $80\ \mathrm{GPa}$ ), and the tube is made of an aluminum alloy ( $G=28\ \mathrm{GPa}$ ). If the shaft has a diameter of $50 \mathrm{~mm}$ and the tube has an outside diameter of $80 \mathrm{~mm}$, find (a) The maximum inside diameter that can be used for the tube if the maximum shearing stress in the tube must be limited to $50\ \mathrm{MPa}$. (b) The maximum inside diameter that can be used for the tube if the rotation of the right end of the shaft with respect to the right end of the tube must be limited to $0.25\ \mathrm{rad}$.

What are valence electrons? Where are they located in an atom? Why are they important?

A radio transmitter emits a time-average power of $5.0 \mathrm{~kW}$ in the form of a radio wave with uniform intensity in all directions. What are the amplitudes of the electric and magnetic fields of this radio wave at a distance of $10 \mathrm{~km}$ from the transmitter?

Match the following terms with the definitions.

$$\begin{array}{llll} \text { atresia } & \text { dystocia } & \text { metrormagia } & \text { pyosalpinx } \\ \text { breech } & \text { eclampsio } & \text { oligomenorrhea } & \text { retroversion } \\ \text { choriocarcinoma } & \text { fibroids } & \text { pathogen } & \text { sterility } \\ \text { Down syndrome } & \text { gestation } & \text { primigravida } & \text { septicemia } \\ \text { dyspareunia } & \text { menarche } & \text { primipara } & \text { trichomoniasis } \end{array}$$

benign uterine tumor composed of muscle and fibrous tissue _______.

Calculate the total number of electrons that can occupy
three p orbitals.

Muscle physiologists study the accumulation of lactic acid [CH3CH(OH)COOH] during exercise. Food chemists study its occurrence in sour milk, beer, wine, and fruit. Industrial microbiologists study its formation by various bacterial species from carbohydrates. A biochemist prepares a lactic acid-lacte buffer by mixing 225 mL of 0.85 M lactic acid (Ka = $1.38 \times 10 - 4$) with 435 mL of 0.68 M sodium lactate. What is the buffer pH?