Use the position function s(t) = -4.9t2 +500, which gives the height (in meters) of an object that has fallen for t seconds from a height of 500 meters. The velocity at time t = a seconds is given by the following.s(a) - s(t)a tlimFind the velocity of the object when t = 3. (Round your answer to one decimal place.)m/s

Answered: Image /qna-images/answer/53e26b65-74d6-49c3-8a1b-3c297541a210.jpg

Answered: Use the position function s(t) = -4.9t2…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Similar questions

If a bullet from a pistol is fired straight up from the ground, its height t seconds after it is fired will be s (t) = -16t2 + 1280t feet (neglecting air resistance). a. Find the velocity function b. How long will it take the bullet to fall back to the ground? c. With what velocity will the bullet hit the ground?
During Ricardo noticed an ink stain with a diameter of about 3 cm on the front of his teacher’s shirt. He then noticed that there was a pen in the pocket and that the ink blot was continuing to spread across the front of the teacher’s shirt. He estimated that the diameter of the ink blot seemed to be growing by about 0.5 cm every 2 minutes. a) Write an equation for the RADIUS, r, of the ink stain, as a function of time, t. Assume that t = 0 represents the time that Ricardo first noticed the ink stain. b) Write an equation showing the AREA, A, of the ink stain as a function of the time t. (Hint: It might help to first write A as a function of r. ) c) Draw a graph of the function A(t) for 10 minutes. d) At what time is the area of the ink stain about 25 square centimeter? Show how you answer this question. (i.e. ”I found it using desmos” is not sufficient)
The amount of growth of plants in an ungrazed pasture is a function of the amount of plant biomass already present and the amount of rainfall.t For a pasture in the arid zone of Australia, the following formula gives an approximation of the growth. Y = -55.12 - 0.01535N - 0.00056N? + 3.946R Here Ris the amount of rainfall, in millimeters, over a 3-month period, Nis the plant biomass, in kilograms per hectare, at the beginning of that period, and Y is the growth, in kilograms per hectare, of the biomass over that period. (For comparison, 100 millimeters is about 3.9 inches, and 100 kilograms per hectare is about 89 pounds per acre.) Now we consider the amount of growth Y as a function of the amount of plant biomass N already present. (a) First we assume that the rainfall is 80 millimeters, so R = 80. (1) Find a formula for the growth Y as a function of the amount N of plant biomass already present. kg/ha (ii) Make a graph of Y versus N. Include biomass levels N from 0 to 800 kilograms…
A runner runs in a straight line and their distance traveled at time t is given by the formula d(t)=3t-0.05t2, where distance is in feet and t is in minutes. Find the runners' average speed during the 2-minute interval beginning at time t=1. ANSWER: ________ feet per minute If rounding is necessary, round to two digits after the decimal.

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