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Let f be defined as follows. y = f(x) = x^2-4x (a) Find the average rate of chan

ID: 2880957 • Letter: L

Question

Let f be defined as follows. y = f(x) = x^2-4x (a) Find the average rate of change of y with respect to x in the following intervals. from x = 5 to x = 6 from x = 5 to x = 5.5 from x = 5 to x = 5.1 (b) Find the (instantaneous) rate of change of y at x = 5. A hot-air balloon rises vertically from the ground so that its height after t sec is given by the following function. h = 1/2 + 1/2 t ft where (0 lessthanorequalto t lessthanorequalto 60) (a) What is the height of the balloon at the end of 43 sec? (b) What is the average velocity of the balloon between t = 0 and t = 43? (c) What is the velocity of the balloon at the end of 43 sec?

Explanation / Answer

h= (1/2)t2+ (1/2)t

a. when t=43 secs

h= (1/2)432+ 43/2 =946 ft

b.

at t=0, h=0

And at t=43, h= 946

average velocity= 949-0/43-0=22ft/sec

c. after 43 secs, velocity is dh/dt= t+1/2=43.5 ft/sec