- Evaluate
- The number 10,000 is a sum of a series of 25 consecutive even integers. What is the smallest number in that series?
- You are running in a path made up of semicircles that are 40 feet in diameter as shown. If you're running at 5 miles per hour, how long will it take to run one mile?

Hint: 1mi = 5280ft. - Evalutate .
- A pendulum's height is represented by the function , where
*t*represents time in seconds since the pendulum was dropped and*f(t)*represents the pendulum's distance from its equilibrium position (that is, the position the pendulum is in when it is not moving) in centimeters. Find a function*g(t)*that represents the speed of the pendulum in meters per second. - A cube's volume is increasing at a rate of 18m
^{2}per second. The cube's volume is currently 8m^{2}. How fast is the cube's surface area increasing in meters per second? - A surface of revolution is created by revolving the function around the x-axis, where See image. a) Find the volume of this figure.

b) Find the surface area of the figure.

c) Bonus question: what is the special name for this particular surface of revolution? - When an object is falling on earth, its velocity in meters per second is represented by the equation , where
*v*is a function representing velocity in m/s and ,*t*represents time in seconds, and*m*represents mass in kilograms. Suppose you drop an object weighing 4 kilograms. After 5 seconds, how fast is it soeeding towards the ground in m/s?

BONUS:
a) Justin Bieber is pushed off a cliff. His fall is represented by the equation , where *y* represents his verticle distance above the ground and *x* represents horizontal distance away from the cliff, both in meters. What is the lenght of Bieber's fall?

b) What does Beethoven think of all this ( ͡° ͜ʖ ͡°) ?