- 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 18m2 per second. The cube's volume is currently 8m2. 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 ͡°) ?