Algebra 2H
Review- Final Exam
Name:____________________________________
Date:_____________________________________
Topics:
 Factoring and Rational Expressions
 Functions
o Linear
o Quadratic
o Absolute Value
o Radical
o Log
o Exponential
o Piecewise



Functions cont’d
o Log
o Exponential
o Piecewise
Trig
o Basics
o Identities
o Graphs & Equations
Sequences and Series
Helpful tips:
Be prepared to:
1. solve any equation in more than one way (algebraically, graphically, and/or algorithmically).
2. explain your reasoning using complete sentences
3. check your answers to see if they make sense (ex: plane’s velocity in flight = 4mph, etc.)
4. use given statements/facts to draw conclusions (logical reasoning)
5. derive various formulas
6. verify trig id’s using multiple approaches
7. explain calculator processes
----------------------------------------------------------------------------------------------------------------------------- ---------------------Factoring
Perfect Square Trinomial
To factor a perfect square trinomial follow the steps below:
1) Create two empty binomials as indicated on the right
(
)(
)
2) Take the square root of the first term of the given trinomial
3) Take the square root of the last term of the given trinomial
4) Take the result of step 2 and put in the 1st position in each binomial
5) Take the result of step 3 and put in the 2nd position in each binomial
6) The signs in the binomials should be the same as the middle term of the binomial
Example 1:
factor : 4 x 2  12 x  9
Answer: (2x - 3)2
a b
Difference of Two Squares
To factor a difference of two squares follow the steps below:
1) Create two empty binomials as indicated on the right
(
)(
)
2) Take the square root of the first term of the given binomial and put in the 1st position of each binomial
3) Take the square root of the last term of the given binomial and put in the 2 nd position of each binomial
4) Make one binomial a sum and the other binomial a difference
2
Example 2:
2
9 x 2 y 2  16
Answer: (3xy - 4) (3xy + 4)
a b
Sum of Two Squares
The sum of squares is not factorable
2
2
Sum of Two Cubes
To factor a sum of two cubes follow the steps below:
1) Create an empty binomial and an empty trinomial as indicated on the right (
)(
)
2) Take the cube root of the first term of the given expression and put it in the 1 st position in the binomial. Square it and put
it in the first position of the trinomial.
**note- ignore all signs until the last step**
3) Take the cube root of the last term of the given expression and
a. put it in the 2nd position in the binomial
b. square it and put it in the last position of the trinomial
4) Find the product of the terms in the binomial and put it in the middle position of the trinomial
5) Arrange the signs as follows ( + )( − + )
Example 3:
8 x 3  27
Answer: (2x + 3) (4x2 - 6x + 9)
1
Difference of Two Cubes
The only difference between a difference of two cubes and a sum of two cubes is the sign arrangement.
Arrange the signs as follows ( − )( + + )
Example 4:
64 z 6  x 3
(4z2 - x) (16z + 4xz + x2)
Answer:
Factoring by Grouping
Steps:
1) Find a convenient point in the polynomial to partition
2) Factor within each group
3) Factor across the groups
Example 5:
( x3 + 7x2 ) + ( 2x + 14)
x2( x + 7) + 2(x + 7)
(x+7) (x2 + 2)
Answer:
Factoring a Trinomial with Leading Coefficient not = 1 in the form ax2+ bx + c
Steps:
1) Multiply the a term by the c term
2) Find the factors of (ac) which will add to the b term
3) Rewrite the b term as the sum of two x terms with coefficients being the factors of (ac)
4) Group the first two terms and the last two terms each in a set of parentheses
5) Factor out greatest common factor from each group
Example 6:
2x3 + x2 + 8x + 4
(2 x3 + x2 ) + (8x + 4)
x2( 2x + 1) + 4(2x + 1)
Answer:
(2x + 1) (x2 + 4)
Multiplying Rational Expressions:
Steps:
 Factor each numerator and denominator completely
 Cancel any like factor in any numerator with any like factor in any denominator
 Multiply the remaining expressions in each numerator
 Multiply the remaining expressions in each denominator
 Reduce if possible
y2  y y2  4

y  2 y 2  3y

y ( y  1) ( y  2)( y  2)


y2
y ( y  3)
Answer:
y( y  1)( y  2)
y( y  3)
Answer:
 (b  2)
(b  3)
Dividing Rational Expressions:
Steps:
 Multiply the first fraction by the reciprocal of the second (KCF)
 Continue using the rules for Multiplying Rational Expressions:
b2
1


2
b 9 3b
b2
3b


(b  3)(b  3) 1
Adding and Subtracting Rational Expressions
Steps:
 Factor all denominators
 Find the least common denominator among all fractions (if none already exists)
 Multiply each denominator and denominator by an appropriate factor to make it equivalent to the LCD
 Combine all numerators (make sure the signs are placed appropriately), simplify and put over LCD
 Reduce if possible
 Combine each set of rational expressions and simplify.
2
Examples
x
2
x
2
x( x  3)  2( x  3)
x 2  3x  2 x  6






x 2  x  6 x 2  5x  6
( x  3)( x  2) ( x  3)( x  2)
( x  3)( x  2)( x  3)
( x  3)( x  2)( x  3)
x 2  5x  6

( x  3)( x  2)( x  3)
( x  6)( x  1)
( x  3)( x  2)( x  3)
Answer:
Functions
1.
Which graph of a relation is also a function?
(a)
2.
(b)
(c)
(d)
Determine the Domain and Range of:
b.
g ( x)  x 2  9
3.
Find the x and y intercepts for the following linear equations:
x  3y  7
a.
b.
3 x  4 y  12
4.
Write and graph the equation of the line given the following information:
m  3, and passes through (3,2)
a.
b.
passes through (5,1) and (2,0)
a.
f ( x)  3x  4
5.
Write & graph the equation of the line that is parallel to y  3 x  2 and passes through (4,1).
6.
Write and graph the equation of the line that is perpendicular to y  3 x  2 and passes through its x intercept.
7.
If the following graph is y = f(x), what is the value of f(1)?
(a) -1
8.
9.
(b) -2
(c) 1
(d) 2
Given f(x) = 4x – 7 and g(x) = 2x – x2, evaluate f(2) + g(-1)
Which function is not one to one?
(a)
(b)
(c)
(d)
3
10.
Which function is not onto?
(a)
(b)
(c)
(d)
f ( x)  3x  4; g ( x)  x 2  9 , find ( f  g )( x) and ( g  f )( x) .
11.
Given
12.
Find the inverse of the following and state the domain.
a.
f(x) = 5x + 2
f ( x) 
b.
4
x3
f ( x)  3x  4; g ( x)  x 2  9 and determine the domain of the result.
13.
Perform the four basic operations on
14.
Complete the following transformations on graph paper. Label your images.
a.
rx axis (2,1)
b.
D2 [ f ( x)  x 2  1]
c.
R0,90 [ g ( x)  2 x  1]
d.
T2,3 [h( x)  2 x 2  4 x  2]
Review- Absolute Values, Inequalities, Piecewise and Variation
Graph each of the following:
1.
2 x  y  1
2.
2 y  2  2x  4
y
3.
y
x
f ( x)  1 x  2  3
y
x
x
For #4-12, solve and check:
4.
x 1  4
5.
3 y  5
6.
2  3d  d  4
7.
2m  1  2
8.
2x  5  x  1
9.
x  3  3(2 x  1)
10.
x  7x  6
11.
2  3d  d  4
12.
2x  3y  1
4
y
Graph the following:
2 x if x  1
f ( x)  
2 x  1 if x  1
2
13.
x
14.
1
 x  2 if x  2
g ( x)   2
 x 2 if x  2

y
x
15.

2

f ( x )  2 x
1
 x2 1
2
y
if x  3
if  3  x  2
if x  2
x
Quadratics
f ( x)  3 x 2  6 x  1
1.
Graph the equation:
2.
Using the three methods discussed in class, find the roots of
3.
Write
4.
Determine the nature of the roots of: h( x) 
5.
Write the quadratic equation in standard form that has zeroes at x= 2 and x= -9
6.
What are the sum and product of the roots of
7.
Write the quadratic equation in standard form that has roots whose sum and product are 3 and -7, respectively.
8.
Derive: the quadratic formula, the sum of the roots, the product of the roots.
g ( x)  6 x 2  19 x  7
f ( x)  2 x 2  6 x  9 in standard form and state the coordinates of the vertex.
1 2
x  6x  3
2
g ( x)  3 x 2  6 x  9
5
g ( x)  2 x 2  4 x  2
9.
Using the three methods discussed in class, find the roots of
10.
Write
11.
A farmer has 200 yards or fencing available to create a rectangular enclosure for his livestock. Using a stream as one side of
the enclosure, he uses the 200 yards of fencing create three sides to enclose the rectangular area. What is the maximum area
he can enclose under such conditions? What are the dimensions of the enclosure? Justify your answers by showing all work.
Include a diagram of the situation.
12.
13.
f ( x)  4 x 2  6 x  9 in standard form and state the coordinates of the vertex.
Eli Manning has been selected to be the first NFL quarterback to travel to Mars. While there, he throws a football from an
elevation of 6 feet at a speed of 132 feet per second. Assuming the acceleration due to gravity on Mars is 33 feet per second
squared (fictitious):
a)
write the equation that models this situation.
b)
determine the maximum height of the football
c)
find the time it takes to reach that height
d)
determine the height when time equals 1.25 sec
e)
find the time(s) it would take to reach a height of 13 feet
Determine the solution of the following quadratic/linear system using the algebraic method.
2x  y  7
y  2 x 2  5x  7
14.
Determine the solution of the following quadratic/linear system using any method.
y  2x  3
y  x 2  2x  1
15.
State the rules for:
rx  axis , ry  axis , rorigin , Tm ,n , Dm
g ( x)  3( x  1) 2  4 write equations, in standard form, for:
T1, 3 g ( x), rx  axis g ( x), ry  axis g ( x), rorigin g ( x), D1 g ( x)
16.
Given
17.
Solve and graph: 2 x  7 x  4  0
8
2
Systems and Matrices
Solve the following systems of equations or inequalities graphically:
1.
2x + 3y = 12
2x - y = 4
2.
x + 3y  15
4x + y < 16
3.
y <½ x + 2
4.
x 2 + y 2 = 100
y=2-x
8.
x 2 + 2y 2 = 6
x + y =1
y  x 2 - 2x
Solve the following systems of equations algebraically:
5.
9.
4x - y = - 20
x + 2y = 13
6.
4x + 5y = 7
3x - 2y = 34
7.
8x - 2y = - 6
y = x 2 + 2x - 5
Graph the following system of inequalities, name the coordinates of the vertices of the feasible region, and find the maximum
and minimum values of the given function for this region:
x + 4y  12
3x – 2y  -6
x + y  -2
3x – y  10
f(x, y) = x – y + 2
6
For questions 10 – 15, only an algebraic solution will be accepted.
10.
At a school dance, the student body charged $3 for couples and $2 for singles. 365 tickets were sold and the total receipts were
$925. Determine the number of each type of ticket sold.
11.
At a student bake sale, cakes were sold for $4 each and pies were sold for $5 each. The students sold a total of 75 cakes and
pies, which made a total of $340. Determine the number of cakes and pies that were sold.
12.
Two dump trucks have capacities of 10 tons and 12 tons. They make a total of 20 round trips to haul 226 tons of topsoil for a
landscaping project. How many round trips does each truck make?
13.
At a discount movie store, Jenny purchased 3 VHS tapes and 4 DVD’s for a total of $57. Jason purchased 11 DVD’s and 7
VHS tapes for a total of $148. Determine the cost of each item.
14.
Sally purchased 4 boxes of Sugar Squares cereal and 3 boxes of Choco-Sticks cereal for $40.75. May purchased 1 box of Sugar
Squares and 4 boxes of Choco-Sticks for $27.25. How much more expensive is a box of Sugar Squares than a box of ChocoSticks?
15.
A fence around a rectangular piece of property is 156 yards long. If the area of the property is 1505 square yards, what are the
dimensions of the property?
For questions 16 – 18, your answer must include a graph and all relevant work.
16.
Tanya plans to start her own business manufacturing sunglasses. She knows that her start-up costs are going to be $3000 and
that each pair of sunglasses will cost her at least $2 to manufacture. In order to remain competitive, Tanya cannot charge more
than $5 per pair of sunglasses. Find how many sunglasses Tanya must sell in order to make a profit.
17.
Kiki earns $7 per hour working at a video store and $10 per hour babysitting. She must work at least 4 hours per week at the
video store, but the total number of hours she can work at both jobs cannot be greater than 15. Determine Kiki’s maximum
weekly earnings.
18.
The available parking area of a parking lot is 600 square meters. A car requires 6 square meters of space, and a bus requires 30
square meters of space. The attendant can handle no more than 60 vehicles. A car is charged $3 to park and a bus is charged
$8. Determine how many of each the attendant should accept to maximize income.
1 3 2
19.
1 2
Find the determinant:
5 3
20.
Find the determinant:
21.
Find the inverse of:
1 2
5 3
22.
Solve #10-14 by Cramer’s Rule or Inv. Matrix Method
3 3 3
4 3 5
x yz 6
23.
Solve for x,y,z. 2 x  y  4 z  15
5 x  3 y  z  10
7
Exponential Functions
1.
The bear population at Yellowstone National Park has been declining since 2005. The rate of decrease
has been determined to be 30% per year. If the initial population was 4000 bears, what is the current bear population (2009)?
2.
What interest rate compounded monthly is required for a $2,500 investment to triple in 10 years?
3.
Jessica made an investment in an account that compounds continuously at a rate of 5.75%. Determine how much time, to the
nearest year, is required for her investment to double.
4.
What interest rate (to the nearest hundredth of a percent) compounded annually is required for an $8,000 investment to grow
to $13,000 in 9 months? Is this a reasonable rate?
5.
There is a population of 3,000 gophers living on various golf courses in the tri-state area. If the number of gophers is
increasing at an average rate of 9.2% per year, predict the population after six years.
6.
Solve for x.
a.
3x1  27 x3
b.
i2
log
12
3x  5 x1
a2
log b 2
b
c.
( x  1)6  729
9.
log 4 8  log 4 2  ?
3
7.
Simplify:
10.
The population of Katonah was 11,020 in 2005 and was growing at a rate of 1.1% per year. Assuming that the population of
Katonah continues to grow at the same rate, find Katonah’s projected population in the year 2010.
a) 12,294
11.
c) 28,583
d) 11, 640
b) by 2000
c) by 2008
d) by 2004
A sum of money is invested at a certain annual interest rate, compounded continuously. After 10.2 years, the investment has
doubled. At what interest rate was the money invested?
a) 5.7%
13.
b) 13,438
Simplify:
In January 1995, the 6,230 residents of Floodplains begin leaving at a rate of 60% per year. If the at rate stays constant, when
will there be less than 100 residents?
a) by 1996
12.
8.
b) 8.3%
c) 6.8%
d) 2.9%
Mike invests $2,000 at 4.5% interest compounded continuously. What is the value of his investment after 6 years?
a) $3,297.44
b) $2,619.93
c) $2,866.66
d) $29,759.46
14.
In reference to #13, how much money would Mike lose if he chose to compound his interest daily over the same period of
time?
15.
Suppose the value of a laptop computer depreciates at a rate of 12.3% a year. Determine the value, to the nearest cent, of a
laptop computer four years after it has been purchased for $3,650.
16.
Andre made an investment in an account that compounds continuously at a rate of 5.75%. Determine how much time, to the
nearest year, is required for his investment to triple.
17.
What interest rate (to the nearest hundredth of a percent) compounded annually is required for an $18,000 investment to grow
to $49,500 in 6 years?
8
18.
When Grandma was planning for her retirement, she found an account that earned 4.6% interest compounded monthly. If she
made her investment back on January 1, 1984, in what year will the single deposit double in her account?
19.
The number of rabbits living in Mathematical Meadow doubles every month. If there are 80 rabbits present initially:
a.
Express the number of rabbits as a function of the time t.
b.
c.
Using your answer from part (a), find how many rabbits are present after 1 year?
Using your answer from part (a), find, to the nearest month, when will there be 10,000 rabbits?
Trigonometry- Basics, Laws of Sines/Cosines & Graphs
Find the exact value of each expression:
1.
cos 270º
2.
sin 90º
7
and sin   0 .
8
3.
Without finding , find the exact value of tan  if cos   
4.
Find the values of the three trigonometric functions for angle  in standard position if a point with the coordinates (-3, -5) lies
on its terminal side.
5.
Given the following triangle find the measure of angle  exactly

3
6
8
and tan   0 .
9
6.
Without finding , find the exact value of cos  if sin   
7.
Find the values of the three trigonometric functions for angle  in standard position if a point with
the coordinates (5, -4) lies on its terminal side.
8.
Find the length of the missing side and the exact value of the three trigonometric functions of the angle  in each figure:
a)
b)
c)

5
3

12
e)
13
9.
9
7

11
Find the exact value of each expression without using a calculator:
a.
10.
7
2

d)

8
sin 150
b.
cos 210
c.
cos 315
Two adjacent apartment buildings in Geometry Garden Estates share a triangular courtyard. They plan to install a new gate
to close the courtyard that forms an angle of 1048 with one building and an angle of 4820 with the second building, whose
length is 527 feet.
a.
Find, to the nearest tenth, the area of the courtyard.
b.
Find, to the nearest tenth, the length of this new gate.
9
11.
A lamppost tilts toward the sun at a 2 angle from the
vertical and casts a 25 foot shadow. The angle from the
tip of the shadow to the top of the lamppost is 45. Find
the length of the lamppost to the nearest tenth of a foot.
2
45
25 ft
12.
A derrick at the edge of a dock has an arm 25 meters long
that makes a 122 angle with the floor of the dock. The arm
is to be braced with a cable 40 meters long from the end of
the arm back to the dock. To the nearest tenth of a meter,
how far from the edge of the dock will the cable be
fastened?
40 m
25 m
122
13.
Using the picture seen to the right, and rounding to the nearest tenth of a meter, find the
height of the tree.
110
23
120 m
14.
Solve ABC if c = 49, b = 40, and A = 53 (round each answer to the nearest tenth)
15.
Solve ABC, to the nearest tenth, if A = 50, b =12, and c = 14 & find the area.
16.
Solve ABC, to the nearest tenth, if A = 85, a =12, and c = 15
17.
Solve ABC, to the nearest tenth, if A = 42, a =8, and b = 9
18.
Determine the area of a rhombus, to the nearest tenth, if the length of a side is 24 inches and one of its angles is 32.
19.
In parallelogram ABCD, AD = 10, AB = 12, and diagonal BD = 18. To the nearest minute, find the measure of angle A.
20.
A side of rhombus ABCD measures 100 feet. The measure of ABC = 11020.
a.
Find, to the nearest foot, the measure of diagonal AC.
b.
Find, to the nearest square foot, the area of rhombus ABCD.
21.
Two consecutive sides of a parallelogram are 6 centimeters and 4 centimeters.
a.
If the length of the longer diagonal of the parallelogram is 9 centimeters, find the measure of the largest angle of the
parallelogram to the nearest degree.
b.
Using your answer from part (a), find the area of the parallelogram to the nearest square centimeter.
22.
Find each of the following exactly:
a.
 
sec 
6
b.
 5 
cot 

 4 
c.
csc(300)
10
23.
24.
25.
Write a sine function with each given period, phase shift, and vertical translation:
a.
period = 2,
phase shift = 
b.
period = 8,
phase shift = -,
vertical translation = 12
vertical translation = -2
Write a cosine function with each given period, phase shift, and vertical translation:
a.
period = ,
phase shift = 
b.
period = 4,
phase shift =

,
4
vertical translation = -1

,
8
vertical translation = 5
State the amplitude, period, phase shift, and vertical translation for each function:
a.
b.
26.

,
2
y  2 cos 0.5 x  3
2
3
y  cos
x
3
7
y  cos x     4
   x  
A=
P=
PS =
VT =
A=
P=
PS =
VT =
y
x

27.
28.
y  2 sin 4x  2 
x 
y  2 cos     1
2 2
   x  
   x  
y

x

x
y
11
29.
30.
x 
y  2 sec   
2 2
   x  


y  csc  2 x  
2

y

x

x

x
   x  
y
31.
   x  
y  cot 2 x
y
Trigonometry- Identities and Equations
USE THE SUM OR DIFFERENCE IDENTITIES TO FIND THE
EXACT VALUES OF EACH TRIGONOMETRIC EXPRESSION:
1. cos 74 cos 44  sin 74 sin 44


tan 110  tan 50
2.
1  tan 110 tan 50
3. cos 345
4. sin195



USE THE HALF-ANGLE IDENTITIES TO FIND THE EXACT
VALUES OF EACH TRIGONOMETRIC EXPRESSION:
5. cos 112.5
6. sin165


7. tan 105


12
Verify Each Identity
8.
1
1

 2 sec 2 x
1  sin x 1  sin x
9.
cos x  sin x
 1  tan x
cos x
10.
1  cos 2 x
 2 csc 2 x  1
2
sin x
11.
ln tan x   ln cot x
12.
2 tan x  sin 2 x
 sin 2 x
2 tan x
13.
cos 4 x  sin 4 x  cos 2 x
14.
2 sin x cos x  2 sin x cos x  sin 2 x
15.
1  sin x
cos x

cos x
1  sin x
16.
1  tan 2 x
cos 2 x 
1  tan 2 x
17.
4 cos 2 x  2
cot x  tan x 
sin 2 x
18.
 1  cot x 


 csc x 
20.
1  sin x
cos x

cos x
1  sin x
22.
cos(u  v)
 tan u  cot v
cos u sin v
24.
tan m  tan n 
26.
log(cos x  sin x)  log(cos x  sin x)  log cos 2 x
27.
28.
1  sin x
 (sec x  tan x) 2
1  sin x
29.
sec 4 s  tan 2 s  tan 4 s  sec 2 s
30.
tan x  cot x
1

sec x  csc x cos x  sin x
31.
tan x  cot x  (sec x  csc x)(sin x  cos x)
32.
tan x  sin x
x
 sin 2
2 tan x
2
33.
cos 3   sin 3  2  sin 2

cos   sin 
2
34.
1  cos 5 x cos 3x  sin 5 x sin 3x  2 sin 2 x
35.
cos 2  cot 2   cot 2   cos 2 
3
3
2
 1  sin 2 x
sin( m  n)
cos m cos n
19.
ln sec x  tan x   ln sec x  tan x
21.
2 sin 2  cos 2   cos 4   1  sin 4 
23.
tan 3t  tan t
2 tan t

1  tan 3t tan t 1  tan 2 t
25.
tan( x  y ) 
cot x  cot y
cot x cot y  1
tan y  sin y
y
 cos 2
2 tan y
2
13
FIND ALL SOLUTIONS OF EACH EQUATION FOR THE GIVEN INTERVAL:
36.
4 cos x  1, 0  x  360
37.
2 cos x  1  0, 0  x  
38.
sin 2x  sin x  0, 0  x  2
39.
cos2 x  sin2 x  sin x, 0  x  360
40.
sin 2x  3 sin x, 0  x  2
41.
2 sin2 x  cos x  1, 0  x  360
42.
2 sin x  tan x  0, 0  x  2
43.
2 sin2 x  5 cos x  1  0, 0  x  360
44.
cos 2x  3 cos x  1  0, 0  x  180
45.
3 cos 2x  5 cos x  1, 0  x  360
46.
9 tan 2 x  3  0, 0  x  
47.
4 cos 2 x  9 cos x  9  0, 0   x  360 
48.
sin 2 x  4(1  2 cos x), 0  x  2
2

Trigonometric Applications
1.
A sector has an arc length of 6 feet and a central angle of 1.2 radians.
a.
Find the radius of the circle.
b.
Find the area of the sector.
2.
A sector has an area of 15 square inches and a central angle of 0.2 radians.
a.
Find the radius of the circle to the nearest tenth.
b.
Find the arc length of the sector to the nearest tenth.
3.
Find the measure of a central angle  (in radians) opposite an arc of 3 meters in a circle with a radius of 1 meter.
4.
Given a central angle of 20, find the length of the radius of the circle, to the nearest tenth, whose intercepted arc has a length
of 40 cm.
5.
Given a central angle of 18, find, to the nearest tenth, the length of its intercepted arc in a circle of radius 5 feet.
6.
Find the diameter of a circle, to the nearest tenth, if an arc is 1.5 feet long and is intercepted by a central angle of 45.
7.
Steve rides his bike 3.5 kilometers. If the radius of the tire on his bike is 32 centimeters, determine the number of radians
that a spot on the tire will travel during the trip.
8.
Two gears are interconnected. The smaller gear has a radius of 3 inches, and the larger gear has a radius
of 7 inches. The smaller gear rotates 250. Through how many degrees, to the nearest tenth, does the
larger gear rotate?
9.
Using the accompanying diagram, find the area of the shaded region, to the nearest tenth, if a pentagon is inscribed in a circle
that has a radius of 3.82 feet.
10.
A regular octagon is inscribed in a circle with radius of 5 feet. Find the area of the octagon to the nearest tenth.
14