Solve each problem using a quadratic equation.
51.A certain bakery has found that the daily demand for blueberry muffins is where pis
the price of a muffin in cents. The daily supply is Find the price at which sup-
ply and demand are equal.
52.In one area the demand for compact discs is per day, where Pis the price in dollars
per disc. The supply is per day. At what price, to the nearest cent, does supply
equal demand?
53.The formula gives the amount Ain dollars that Pdollars will grow to in
2 yr at interest rate r(where ris given as a decimal), using compound interest. What
interest rate will cause $2000 to grow to $2142.45 in 2 yr?
54.Use the formula to find the interest rate rat which a principal Pof
$10,000 will increase to $10,920.25 in 2 yr.
A=P 11 +r 22
A=P 11 +r 22
5 P- 1
700
P
3 p-200.
3200
p ,
530 CHAPTER 9 Quadratic Equations, Inequalities, and Functions
55.Rhinoceros: ;
Froude number
56.Triceratops: ;
Froude number=0.16
/=2.8
=2.57
/=1.2
Recall that corresponding sides of similar triangles are proportional. Use this fact to find the
lengths of the indicated sides of each pair of similar triangles. Check all possible solutions in
both triangles. Sides of a triangle cannot be negative (and are not drawn to scale here).
57.Side AC 58.Side RQ
C
AB
3 x – 19 x – 4
x – 3 4
F
DE
PR
Q
S U
T
x + 3^3 x – 11
x – 5
3
Total spending ( in billions of dollars) in the United States from all sources on physician and
clinical services for the years 2000 –2007 are shown in the bar graph on the next page and
can be modeled by the quadratic function defined by
Here, represents 2000, represents 2001, and so on. Use the graph and the model
to work Exercises 59 – 62. See Example 6.
x= 0 x= 1
ƒ 1 x 2 =0.3214x^2 +25.06x+288.2.
William Froude was a 19th century naval architect who
used the expression
in shipbuilding. This expression, known as the Froude
number,was also used by R. McNeill Alexander in his re-
search on dinosaurs. ( Source: “How Dinosaurs Ran,”
Scientific American,April 1991.) In Exercises 55 and 56,
find the value of v (in meters per second), given
g=9.8 m per sec^2. (Round to the nearest tenth.)
v^2
g/
