Find the length of

$$\overline { A B }$$

and the midpoint of

$$\overline { A B }$$

. Round the length of

$$\overline { A B }$$

to the nearest tenth. A(8, 11) and B(-5, 2)

Use a CAS to evaluate the integral in two ways: (i) integrate directly; (ii) use the CAS to find the partial fraction decomposition and integrate the decomposition. Integrate by hand to check the results.

$$\int \frac { x ^ { 2 } + 1 } { \left( x ^ { 2 } + 2 x + 3 \right) ^ { 2 } } d x$$

Evaluate using the appropriate method or combination of methods.

$$\int \frac { \left( x ^ { 2 } - x \right) d x } { ( x + 2 ) ^ { 3 } }$$

The distance d (in meters) of the bob of a pendulum of mass m (in kilograms) from its rest position at time t (in seconds) is given. The bob is released from the left of its rest position, which represents a negative direction. Describe the motion of the object. Be sure to give the mass and damping factor. $d=-20 e^{-0.7 t / 40} \cos (\sqrt{\left(\frac{2 \pi}{5}\right)^{2}-\frac{0.49}{1600}} t)$

Let u, v, and w be vectors and let c be a scalar. Use the component form of vectors to prove the following properties.

$$u*(v+w)=u*v+u*w$$

Solve. 17 + s/15 =-4

The number of students in a chess club decreased from 18 to 12. What is the percent decrease? Round to the nearest percent.

Determine whether each statement makes sense or does not make sense, and explain your reasoning. Limits indicate that a graph can get really close to values without actually reaching them.

A mass connected to an ideal spring is oscillating without friction on a horizontal surface. Sketch graphs of the kinetic energy, potential energy, and total energy as functions of time for one complete cycle.

How can you use the Quotient of a Power Property to explain the definition of

$$x ^ { - n } ?$$

( Hint: Think of

$$\frac { 1 } { x ^ { n } }$$

as

$$\frac { x ^ { 0 } } { x ^ { n } }$$

.)

A converging lens has a focal length of 20 cm. A cup is located 50 cm from the lens. (a) What type of image will be formed? (b) Where will the image be located? Show your calculations.

Evaluate the expression for the given value of the variable. x² - 3 when x = 5

Find a general solution of

$$y ^ { \prime \prime } - i y ^ { \prime } + 6 y = 0$$

A college sends a survey to members of the class of 2012. Of the 1254 people who graduated that year, 672 are women, of whom 124 went on to graduate school. Of the 582 male graduates, 198 went on to graduate school. What is the probability that a class of 2012 alumnus selected at random is female and did not attend graduate school?