Free-Falling Object In Exercises 101 and 102. use the position function s ( t ) = − 16 t 2 + 500 , which gives the height (in feet) of an object that has fallen for t seconds from a height of 500 feet. The velocity at time t = a seconds is given by lim t → a s ( a ) − s ( t ) a − t A construction worker drops a full paint can from a height of 500 feet. How fast will the paint can befalling after 2 seconds?
Free-Falling Object In Exercises 101 and 102. use the position function s ( t ) = − 16 t 2 + 500 , which gives the height (in feet) of an object that has fallen for t seconds from a height of 500 feet. The velocity at time t = a seconds is given by lim t → a s ( a ) − s ( t ) a − t A construction worker drops a full paint can from a height of 500 feet. How fast will the paint can befalling after 2 seconds?
In Exercises 101 and 102. use the position function
s
(
t
)
=
−
16
t
2
+
500
, which gives the height (in feet) of an object that has fallen for t seconds from a height of 500 feet. The velocity at time
t
=
a
seconds is given by
lim
t
→
a
s
(
a
)
−
s
(
t
)
a
−
t
A construction worker drops a full paint can from a height of 500 feet. How fast will the paint can befalling after 2 seconds?
ax+b
The graph of f(x) =
has horizontal tangent at (2, -1). Determine the values of a and b.
Section 3: Thinking
12. The average height of female children from birth to age 16. The equation f(t) =
-115(0.85) + 165, where h is the height in cm and t is the age in years. [3 Marks Each]
a) Find the average rate of change from age 1 to 4.
b) Using the estimation of h = 0.01, find the instantaneous rate of change at age 7.
Пx→4°
#
1
1
[4 Marks]
13. Evaluate the lim,
A mass of 2 kg stretches a spring 0.07 m. The mass is in a medium that exerts a viscous resistance of 23 N
when the mass has a velocity of 2 The viscous resistance is proportional to the speed of the object.
m
-
S
Suppose the object is displaced an additional 0.03 m and released.
m
Find an function to express the object's displacement from the spring's natural position, in m after t
seconds. Let positive displacements indicate a stretched spring, and use 9.8
gravity.
as the acceleration due to
$2
u(t) =
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Chapter 1 Solutions
Student Solutions Manual for Larson/Edwards' Calculus of a Single Variable, 11th
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