Vocabulary: Sex ratio

In the given exercise below, find the centroid of the region.

Region between y=x(a-x) and the x-axis for a>0

Consider the region bounded by the graphs of $y=\ln x, y=0$, and $x=e$. Find the centroid of the region.

True or False. If a function f is continuous on the closed interval [a, b], then f is continuous on the open interval (a, b).

Four lines are represented by the equations below. $\ell: y=-x+1 \quad m: y=-x+7 \quad n: y=2 x+1 \quad p: y=2 x+7$ Graph the four lines in the coordinate plane.

Consider a concentric shaft, fixed axially and rotated inside the sleeve. Let the inner and outer cylinders have radii

$$r_i$$

and

$$r_0$$

, respectively, with total sleeve length L. Let the rotational rate be Ω (rad/s) and the applied torque be M. Using these parameters, derive a theoretical relation for the viscosity μ of the fluid between the cylinders.

Simplify the ratio. 36/18

How many straight lines that pass through the origin are tangent to y = cos x? Find (to 6 decimal places) the slopes of the two such lines that have the largest positive slopes.

What is the ratio of their intensities?

A torque of $0.97 \mathrm{N} \cdot \mathrm{m}$ is applied to a bicycle wheel of radius 35 cm and mass 0.75 kg. Treating the wheel as a hoop, find its angular acceleration.

Consider the region bounded by $y = e^x,$ the x-axis, and the lines x = 0 and x = 1. Find the volume of the solid. The solid obtained by rotating the region about the horizontal line y = -3.

A $4.00 \times 10^{2} \mathrm{N} \cdot \mathrm{m}$ torque is produced applying a force 1.60 m from the fulcrum and at an angle of $80.0^{\circ}$ to the lever. How large is the force?

This problem concerns the region bounded by $y = x^2,$ y = 1, and the y-axis, for $x \geq 0.$ Find the volume of the solid. The solid obtained by rotating the region about the line y = -2.

R.K. is an 85 -year-old woman who lives with her husband, who is 87 . Two nights before her admission to your cardiac unit, she awoke with heavy substernal pressure accompanied by epigastric distress. The pain was reduced somewhat when she rolled onto her side but did not completely subside for about 6 hours. The next night, she experienced the same chest pressure. The following morning, R.K.'s husband took her to the physician, and she was subsequently hospitalized to rule out myocardial infarction (MI). Lab specimens were drawn in the emergency department. She was given $325 \mathrm{mg}$ chewable, non-enteric-coated aspirin, and an IV line was started. She was placed on oxygen $\left(\mathrm{O}_2\right)$ at $2 \mathrm{~L}$ via nasal cannula.

You obtain the following information from your history and physical examination: R.K. has no history of smoking or alcohol use, and she has been in good general health, with the exception of osteoarthritis of her hands and knees and some osteoarthritis of the spine. Her only medications are simvastatin (Zocor), ibuprofen as needed for bone and joint pain, and "herbs." Her admission vital signs (VS) are blood pressure $132 / 84$, pulse 88 , respirations 18 , and oral temperature $99^{\circ} \mathrm{F}\left(37.2^{\circ} \mathrm{C}\right)$. Her weight is $114 \mathrm{lbs}$ $(51.7 \mathrm{~kg})$ and height is $5 \mathrm{ft}, 4$ in (163 cm). Moderate edema of both ankles is present; capillary refill is brisk, and peripheral pulses are 1+. You hear a soft systolic murmur. She denies any discomfort at present. You place her on telemetry, which shows the rhythm in the following figure.

Give at least 2 reasons for inserting an IV line.