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Question: A ball is dropped from the top of the Empire State building to the ground below. The height, y, of the ball above the ground (in feet) is given as a function of time, t, (in seconds) by
y = 1250 - 16t2.
(a) Find the velocity of the ball at time t. What is the sign of the velocity? Why is this to be expected?
(b) Show that the acceleration of the ball is a constant. What are the value and sign of this constant?
(c) When does the ball hit the ground, and how fast is it going at that time? Give your answer in feet per second and in miles per hour (1 ft/sec = 15/22 mph).
Companies try to forge a marketing channel, a set of interdependent organizations involved in the process of making a product or service available for use or consumption by the consumer or business user.
A boat traveled 210 miles downstream and back. The trip downstream took 10 hours. The trip backtook 70 hours. What is the speed of the boat in still water? What is the speed of the current?
Use the Squeeze Theorem to show that limitx →0 √(x3 + x2) sin π/x = 0. Illustrate by graphing the functions f, g, and h (in the notation of the Squeeze Theorem) on the same screen.
A steady stream of water flows into a partially-filled rectangular tank. After 6 minutes, there are 87 gallons of water in the tank. After 21 minutes, there are 222 gallons. Write an equation to represent the volume of water in the tank y after x ..
As you watch the film, take notes on the nonverbal cues that the characters in the film exhibit. Be as descriptive as possible when describing the nonverbal codes you witness throughout the film.
Construct a k-form on S^k with nonzero integral. [Hint: Construct a compactly supported k-form in R^k with nonzero integral, and project stereo graphically.]
Express the negation of the following statement. All negations should be simplified as much as possible. ∀x ∃y (y > 0 → (-2 ≤ x 6))
in a class all pupils take mathematics m 18 take chemistry c 17 take biology b and 24 take physics p of those taking 3
Exercise 3.20: Let Sn = S0 + (sigma from n to i=1 of ξi) be a Random Walk, with P(ξ1 = 1) = p, P(ξ1 = -1) = 1 - p. Show that for any λ, eγSn-λn is a martingale for the appropriate value of γ.
question mrs. dean wants to paint her mailbox formed by a prysm mounted by a half cylinder. the cylinders radius is
Let B be the basis of P3 consisting of the Hermite polynomials in Exercise 21, and let p(t) = - 1 + 8t2 + 8t3.
a. Create the profit function for the hospital. b. What is the average rate of change in the profit from year 3 to year 5?
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