Precalculus #2.4
Practice
Name
1. The height of a baseball in feet / seconds after it has been hit is given by
! = 3+ 4At -16t2. At what time / does the baseball reach maximum height? Give your
answer correct to 3 decimal places.
2. The height of a baseball in fuet / seconds after it has been hit is given by
! =3+35t -16t2. What is the maximum height of the baseball? Give your answer
correct to 3 decimal places.
3
. Suppose a farmer has I 5 5 feet of fence and he wants to enclose a pasture with a
rectangular boundary. There is already fencing along one side of the field that he wants
to enclose, so he will only need to fence 3 sides of the new field. What is the maximum
area that he can fence?
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package is dropped from an airplane and falls to the ground along a parabolic
path, starting at the vertex of the parabola. The package was released when the plane
was directly above a marker at a height of 5 kilometers, and the package hits the ground
4.77 kilometers from the marker. If ft is the height of the package when it is a horizontal
distance d from the marker, the equation for /z in terms of d is given by
4. A relief
h(d) = acl2 +bd + c, where
to 3 places.
airplane
a:
b
-,
:
and c
:
.
Round any decimals
-,
path/truj*r{ory sf relief package
Brown has 119 feet of fence. He wishes to close in a rectangular field using the
bam as one side of the field. Suppose each side of the field perpendicular to the barn
has length x feet.
a) What is the area of the fenced in field in terms of x ?
b) In the context of this problem, what values of x make sense?
c) Approximate the maximum volume of the fenced field.
5. Farmer
6. You wish to pack a cardboard box inside a wooden crate. In order to have room for the
packing materials, you need to leave a .5 ft space around the front, back and sides of the
box and a 1 ft space around the top and bottom ofthe box. Ifthe cardboard box is x feet
long, (x+2) feet wide, and (x-1) feet deep, find a formula in terms of x for the amount of
packing material needed.
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