vasquez (mpv244) – HW07 – Schultz – (56445)
1
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beFore answering.
001
10.0 points
A storm system is headed towards Austin.
The Weather Service O±ce Forecasts that
t
hours aFter midday the storm will be at a
distance oF
s
(
t
) = 8 + 2
t

t
2
miles From Austin. At what speed (in miles
per hour) will the storm be moving when it
reaches Austin?
1.
storm speed = 7 mph
2.
storm speed = 6 mph
correct
3.
storm speed =

7 mph
4.
storm speed =

6 mph
5.
storm speed = 8 mph
6.
storm speed =

8 mph
Explanation:
The storm will reach Austin when
s
(
t
) = (4

t
)(2 +
t
) = 0
,
i.e.
, when
t
= 4.
Now the velocity oF the
storm is given by
s
′
(
t
) = 2

2
t,
the negative sign indicating that the storm is
moving towards Austin. Thus at
t
= 4,
s
′
p
4
P
= 2

8 =

6
.
Consequently, since speed is always non
negative,
storm speed = 6 mph
.
002
10.0 points
IF a rock is thrown vertically upwards From
the surFace oF the planet Newton with an
initial velocity oF 12 Ft/sec, its height aFter
t
seconds is given by
h
= 12
t

1
2
t
2
.
²ind the velocity oF the stone aFter it has risen
70 Feet.
1.
velocity = 2 Ft/sec
correct
2.
velocity = 3 Ft/sec
3.
velocity = 1 Ft/sec
4.
velocity = 4 Ft/sec
5.
velocity = 5 Ft/sec
Explanation:
When the height
h
= 70, then
70 = 12
t

1
2
t
2
.
AFter simplifcation and Factorization this be
comes
t
2

24
t
+ 140 = (
t

10)(
t

14) = 0
.
Thus the rock will have risen 70 Feet aFter 10
seconds. But its velocity is given by
dh
dt
= 12

t .
Consequently, aFter 10 seconds,
velocity = 2 Ft/sec
.
003
10.0 points
²ind the rate at which the surFace area oF a
sphere is changing with respect to its radius
r
when
r
= 4 cm.
1.
rate = 8 cm
2
/
cm
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2
2.
rate = 36
π
cm
2
/
cm
3.
rate = 32
π
cm
2
/
cm
correct
4.
rate = 48 cm
2
/
cm
5.
rate = 27 cm
2
/
cm
Explanation:
For a sphere with radius
r
its
surface area = 4
πr
2
.
Now the rate at which the surface area is
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 Spring '09
 RUTH
 Chemistry, Acceleration, Velocity

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