Evaluate the integral:

$$\int_{\pi / 4}^{\pi / 2}\left(1+e^{\cot \theta}\right) \csc ^{2} \theta d \theta$$

The uranium ores of the Athabasca Basin deposits of Saskatchewan, Canada, are unusually pure, containing up to 70, uranium oxides. Why doesn’t this uranium ore undergo an explosive chain reaction?

A projectile is fired at an inclination of $45^{\circ}$ to the horizontal, with a muzzle velocity of 100 feet per second.The height h of the projectile is modeled by $h(x)=\frac{-32 x^{2}}{(100)^{2}}+x$ where x is the horizontal distance of the projectile from the firing point. Find the maximum height of the projectile.

Factor. 15xy + 35x + 12y + 28

In 2004, 10-year-old Tilly Smith was vacationing with her family at a beach resort in Thailand. She is credited with saving approximately 100 lives shortly after the magnitude 9 Indian Ocean earthquake. How did she save so many people? (1) She told her family to spend an extra week at the beach. (2) She recognized the signs of an approaching tsunami and warned the people. (3) She predicted exactly when the earthquake would occur. (4) She convinced the people to avoid eating before going swimming.

Solve the equation. Check your solution. 18. -2 + j = -22

PRACTICE — Problems 1-36 are the Quick W's that fottow the EXAMPLES, In]

Building Skills In Problems 47-50, use a calculator to write each expression as & oad to two decimal places. See Objective f.

Find all the complex roots. Write roots in rectangular form. If necessary, round to the nearest tenth. The complex fourth roots of 81

$$81 \left( \cos \frac { 4 \pi } { 3 } + i \sin \frac { 4 \pi } { 3 } \right)$$

A company is focus testing a new type of fruit drink. The focus group is 47% male. Of the responses, 40% of the males and 54% of the females said they would buy the fruit drink. What is the probability that a randomly selected person would buy the fruit drink.

In each formula, substitute the given values of the variables. Then find the value of the remaining variable, which is printed in red. Distance an object falls:

$$d = \frac { v ^ { 2 } } { 2 g }$$

; d=1000, v=140

Simplify. Write each answer in standard form.

$$\left( 4 x ^ { 2 } + 9 x + 1 \right) + \left( 2 x ^ { 2 } + 7 x + 13 \right)$$

Determine whether each situation describes a survey, an experiment, or an observational study. Then identify the sample, and suggest a population from which it may have been selected.

A research group randomly selected 80 college students, half of whom took a physics course in high school, and compared their grades in a college physics course.

Describe a different situation in which you would find each representation of a function, including a table, a graph, and an equation, useful.

Consider a series RLC circuit with R = 15 $\Omega$, L = 200 mH, C = 75 $\mu \mathrm { F }$, and a maximum voltage of 150 V. When will the current be greatest: at resonance, at 10% below the resonant frequency, or at 10% above the resonant frequency?