For the following exercises, calculate the center of mass for the collection of masses given. 257. Unit masses at ( x , y ) = ( 1 , 0 ) ( 0 , 1 ) ( 1 , 1 )
For the following exercises, calculate the center of mass for the collection of masses given. 257. Unit masses at ( x , y ) = ( 1 , 0 ) ( 0 , 1 ) ( 1 , 1 )
Let f be defined as follows.
y = f(x) = x² - 5x
(a) Find the average rate of change of y with respect to x in the following intervals.
from x = 4 to x = 5
from x = 4 to x = 4.5
from x = 4 to x = 4.1
(b) Find the (instantaneous) rate of change of y at x = 4.
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Determine whether the inverse of f(x)=x^4+2 is a function. Then, find the inverse.
Velocity of a Ball Thrown into the Air The position function of an object moving along a straight line is given by s = f(t). The average velocity of
the object over the time interval [a, b] is the average rate of change of f over [a, b]; its (instantaneous) velocity at t = a is the rate of change of f at a.
A ball is thrown straight up with an initial velocity of 128 ft/sec, so that its height (in feet) after t sec is given by s = f(t) = 128t - 16t².
(a) What is the average velocity of the ball over the following time intervals?
[3,4]
[3, 3.5]
[3, 3.1]
ft/sec
ft/sec
ft/sec
(b) What is the instantaneous velocity at time t = 3?
ft/sec
(c) What is the instantaneous velocity at time t = 7?
ft/sec
Is the ball rising or falling at this time?
O rising
falling
(d) When will the ball hit the ground?
t =
sec
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Area Between The Curve Problem No 1 - Applications Of Definite Integration - Diploma Maths II; Author: Ekeeda;https://www.youtube.com/watch?v=q3ZU0GnGaxA;License: Standard YouTube License, CC-BY