Andrew Robert Border

Homework 5
due
Fri, Nov 13
at 11:59 pm
Course: math151au09es
This problem set covers Sections 3.9  4.1 of the text.
Recitation Call#: .
Carefully read all instructions for entering answers into WeBWorK.
Set: Hmwk5
1.
(2 pts) Suppose
xy
=
1 and
dy
dt
=

2.
Find
dx
dt
when
x
=
4.
dx
dt
=
2.
(2 pts) A spherical snowball is melting in such a way that
its diameter is decreasing at rate of 0.3 cm/min. At what rate is
the volume** of the snowball decreasing when the diameter is
17 cm? (Note the answer is a positive number).
Rate =
cm
3
min
**) Look up the formula for the volume of a sphere in the front reference
pages of Stewart’s book.
3.
(2 pts) The height of a triangle is increasing at a rate of
1
cm
min
while the area of the triangle is increasing at a rate of 2
cm
2
min
.
At what rate is the base of the triangle changing when the
height is 10
cm
and the area is 95
cm
2
?
Rate =
cm
min
4.
(3 pts) A street light is at the top of a 20 ft tall pole. A
woman 6 ft tall walks away from the pole with a speed of 5
ft/sec along a straight path. How fast is the tip of her shadow
moving when she is 35 ft from the base of the pole?
Rate =
ft
sec
5.
(3 pts)
u
x
4200
A lighthouse is situated on a small island 4200 feet from a
straight shoreline. If the beacon on the lighthouse makes 5 rev
olutions per minute, how fast is the light beam moving along
the shoreline when it is pointing 4000 feet away from the near
est point on the shoreline to the lighthouse?
To solve this problem, we first need to express the distance
x
along the shoreline between the light beam and the nearest point
to the lighthouse, in terms of the angle
u
shown in the above
picture. We find that
x
=
(Your answer should be an
expression in
u
.)
We have that
du
dt
=
radians per minute
and that
dx
dt
=
feet per minute.
6.
(3 pts) A swimming pool is 17 feet wide and has transverse
crosssections which look like:
6
10
6
8
h
5
5
If the pool is being filled at a rate of 0.8 cubic feet per minute,
how fast is the water level rising when the depth of water is 4
feet?
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 Fall '08
 Any
 Math, pts, Imperial units, Convex function, critical numbers

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