Math 10B Test 2
100 pts
November 23, 2009
Professor Evans
Directions:
Answers alone are not sufficient. Show all work. Each problem is worth 20 points.
(1)
On January 2, 2008, Jack was given a $100 savings account and Jane was given a $60 savings
account. On January 2, 2009, Jane was given another $60 savings account. The accounts pay
an annual interest rate of 50%.
True
or
False
:
If Jack and Jane withdraw their money on January 2, 2010, they will each have the same amount.
Justify.
Solution: Jack ends up with 100(1
.
50)
2
= 225 dollars. Jane ends up with 60(1
.
50)
2
+ 60(1
.
50) =
225 dollars. Hence the answer is True.
(2)
The base of a loaf of bread is the region inside the circle
x
2
+
y
2
= 1. Each crosssection
perpendicular to the
x
axis has the shape of a square. (Think of paperthin squareshaped slices
of bread.) Find the volume of the loaf of bread.
Hint
: The answer is between 1 and 8.
Solution: The cross section at any given
x
is a square of side length 2
√
1

x
2
. The area of this
square is 4(1

x
2
). Hence the volume of the loaf is
R
1

1
4(1

x
2
)
dx
= 16
/
3.
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 Summer '10
 reed
 Inch, octagonal base

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