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of the circular ripple spreads at the rate 1.5 ft/sec, how fast is the enclosed area increasing at the end of 2 seconds?
If the balloon goes straight up at the rate of 8 ft/sec, how fast is the distance from the observer to the balloon increasing when the balloon is 50 ft high?
s(t) 16t 200t
2
= − +
feet above the ground.
(a) How high is the rocket after 6 seconds?
(b) What is the average velocity of the rocket over the first 6 seconds of flight (between t=0 and t=6)?
(c) What is the instantaneous velocity of the rocket at t=2 sec?
with an initial velocity of 96 ft/sec.
(a) Find the velocity of the ball at time
the Opera dislocates the chandelier and causes it to fall from rest and crash on the floor.
a. What is the equation of motion of the chandelier?
b. Find the instantaneous velocity of the chandelier at 1 sec and 1.5 sec.
c. Find how long it takes the chandelier to hit the floor.
d. What is the speed of the chandelier when it hits the floor?
The stone rises until it is even with the top of the tree and then falls back to the ground. How tall is the
tree?
function of the skidding car is
(a) Find a formula for L in terms of x and y.
L(x,y)=
b) Find a formula that expresses L as a function of x alone.
L(x)=
(c) What is the domain of the function in part (b)? Express as an interval.
Domain =
defined on the interval [−8.72,1.76].
a.) f(x) is concave down on the region(s)
b.) A global minimum for this function occurs at
c.) A local maximum for this function which is not a global maximum occurs at
d.) The function is increasing on the region(s)
The position of an object moving along a straight line is given by x = 3 − 2t
2 + 4t
3 where x is
in meters and t in seconds.
a) Derive the expressions for the velocity and acceleration of the object as a function of time.
b) Find the position of the object at t = 0, t = 2s, t = 4s.
c) Find the displacement or the object between t = 2s and t = 4s; between t = 0s and t = 4s.
d) Find the average velocity between t = 2s and t = 4s; between t = 0s and t = 4s;
between t = 1s and t = 3s.
e) What is the instantaneous velocity at t = 2s? at t = 5s?
f) At what time(s) is/are the instantaneous velocities zero?
g) When does the instantaneous velocity have a maximum or a minimum value?
h) Find the change in velocity between t = 2s and t = 5s.
i) Find the average acceleration between t = 2s and t = 5s; between t = 1s and t = 3s.
j) Find the instantaneous acceleration of the object at t = 2s; t = 5s.
#340153 on Dec 2023