Sequences & Series Questions and Answers

4 3 b In b ca In In b 2 ln c 32 In a In a syntax incomplete

Find sec 0 if cos 0 02 2 O 7 2 8 2 2 2 07 7 7

a If t determine the quadrant in which the unit circle point P t lies 3 Quadrant I Quadrant II Quadrant III Quadrant IV t lies on the x axis or y axis between quadrants 11 b If s 5 find a real number t in the interval 0 2 such that P t P s Recall that P t and P s represent points on the unit circle

below THANK YOU FOR YOUR HELP Find an equation for the graph sketched below 5 4 3 2 1 8 7 6 5 4 3 2 23 4567 1 2 3 4 5

Solve each equation 3 8 24 4 2In 3x 2 4 5 log 2x log x x

2 A rope to the top making the How tall 3ooft S bong is allached Slag pole 59 S angel an ground is the I Round your answer The Slag with Pole to the nearest enth

Two trees reside to the north The are 24 paces apart From where you stand the right tree is 15 paces away The left tree is 20 paces away You feel that the angle they form will give you the direction you must travel

Maya dropped her keys down a storm drain Her hand was 1 meter above the ground The keys fell 10 meters to the floor of the drain The following equation describes this situation 1 10 9 What does 9 tell us Choose 1 answer The distance between Maya s hand and the floor of the drain was 9 meters The keys fell 9 meters None of the above

Express using rational exponents Provide your answer below

Destiny was testing different apple pie recipes This graph shows how many pounds of apples she used in different recipes Amount of apples XX X X 3 13 4 pounds xxx 3 3 3 Pounds XXX xx X 4 4 3 If you combine all of the apples from the recipes that use exactly 3 pounds of apples how many pounds of apples will you have in all 6 pounds 6 pounds 2 7 pounds

List the angles of each triangle in order from largest to smallest 7 A 8 i

x 2y z 3 2x 4y z 7 2x 2y 3z 4 Solve the following system of equations using matrices x 2y z 3 2x 4y z 7 2x 2y 3z 4 O 4 1 2 0 O 3 1 2 1 O 2 1 2 1 O 3 1 2 2

x y 25 x y 1 Solve the following system O 2 3 1 4 O 4 8 2 4 O 1 2 2 9 O 4 3 3 4

For exercises 4 6 what can you conclude about each of the following from the diagram at the right Explain 4 QM 5 ZTOM and ZNOM 6 the value of MN

Which number line model represents the expression Choose 1 answer 1 T 1 1 3 1 L 15555 1 7100 3 LIT SIN 0 1 1 1 1 0105 0 110 0 155 15 2 4 25 GIN 3 calc 3 45 CHIF 4 1 1155 5

15 Show that T is a linear transformation from R to R by finding a matrix that implements the mapping ED X T x 6x 0 3x x4 X2 X4

Question 1 a A F b C Using the Law of Sines to solve the triangle if ZA ZB is degrees C a 0 1 pt 3 98 36 C 67 b 22 C Round to two decimal places if needed Assume LA is opposite side a ZB is opposite side b and C is opposite side c Question Help Video Message instructor B De

Prove that if and y are sequences of real numbers such that and M 0 k 1 k 1 Hint What can you say about the corresponding finite sums k 1 then kyk

Write an equation for the polynomial graphed below 6 5 4 T y x 3 2 3 2 2 3 4 5 6 2 3 5 Q

Solve the following system of differential equations where x x t and y y t are differentiable functions of a real variablet x y such that x 0 2 and y 0 3 O C O 3 3 1 2 e 6t e 6t 5est 6t e 3 2 1 5e 6t e 6t 2 5est e 6t 5e8t 5e8t est lest 5est 16e 6t 2e8t 24e 6 6t 2est 1 2e 6t 6est 2e 6 4est X 7x 7y Y

If a Camel drank 2 gallons of water every 1 hour how many 24 it drink in one hour gallans did it drink in

8 p 24 A p 3 B p 16 C p 3 10 10 8 6 4 8 10 12 8 6 D p 192 188 14 2 O 190 192 16 18 4 2 0 194 196

Employees can be classified according to gender male female income low medium high and rank assistant instructor dean How many different ways can one person be classified 4 How many ways can four paintings be arranged on a wall 5 How many ways can 3 fraternity members be selected from 10 if one is to be president one is to be vice president and the third is to be treasurer 6 How many different passwords are there if the first character must be a letter and the other three must be digits 7 There are 12 applicants for financial aid The selection comity may choose only 4 How many ways can this be done 8 A candy store allows customers to select 3 different candies to be packed and mailed If there are 13 different types of candy then how many ways can this selection be done

V Find the designated sum of the arithmetic series 1 Se of 3 7 11 15 2 Sof 13 11 9 7 VI Find the designated sum of the geometric series 1 S of 4 8 16 32 2 S13 of 1 6 36 216 VII Determine if each INFINITE geometric series converges has a sum or diverges does not have a sum 1 a 45 r 1 5 2 a 5 4 r 2 1 3 a 13 r 1 2 4 a 2 r 3 5 a 3 r 3 5 6 a 2 r 4 3 VIII Evaluate each infinite geometric series described If it diverges state that 1 32 16 8 4 2 1 15 125 1 125 3 2 4 8 16 4 3 1 1 3 1 9

III Determine if the sequence is arithmetic or geometric and then find the next three terms 1 2 4 8 16 2 65 60 55 50 45 IV Determine if the sequence is arithmetic or geometric and then find the given term 1 11th term 5 3 1 1 3 6th term 25 75 225 675 4 22nd term 2 5 8 11 14 5 10th term a1 320 r 0 5

You may use your notes and a calculator You must show all Work 1 Fill in the blanks for these arithmetic sequences 1 Find the next three terms 3 10 17 24 31 38 45 52 2 Find the 25th term 53 50 47 44 41 II Fill in the blanks for these geometric sequences 1 Find the next three terms 128 64 32 16 8 2 Find the 9th term 0 01 0 1 1 10 100 III Determine if the sequence is arithmetic or geometric and then find the next 1 2 4 8 16 2 65 60 55 50 45 IV Determine if the sequence is arithmetic or geometric and then find the given term 1 11th term 5 3 1 1 3 6th term 25 75 225 675 4 22nd term 2 5 8 11 14 term 5 10th term a1 320 r 0 5

A spring is attached to the ceiling and pulled 11 cm down from equilibrium and released After 4 seconds the amplitude has decreased to 9 cm The spring oscillates 16 times each second Assume that the amplitude is decreasing exponentially Find an equation for the distance D the end of the spring is below equilibrium in terms of seconds t D t

Use power series to solve the initial value problem Answer y 00 00 2 27 1 2n 1 x y 3xy 3y 0 y 0 1 y 0 0

4 What is the current concentration of CO2 in Earth s atmosphere in units of parts per million When in the last 1000 years has the CO2 level been this high

Find the area of the region bounded below by the x axis and above by the curve T 2 sin 0 y 4 sin 0 tan 0 with 0 0 2

term the leading coefficient and the degree of the polynomial f x 18x 4 12 0 15x 2 5x

jun wn 40 600 J 60 a a XB B 8c Round to nearest tenth

Use the graph of g x to answer each question 10 9 8 7 6 5 4 3 2 1 Domain Range 10 9 8 7 6 NW sa G Increasing 5 2 3 4 5 6 7 8 9 10 a Find the domain and range of g x Write the answers in interval notation 40 2 1 2 3 4 5 6 7 8 9 10 b Evaluate Enter DNE if value does not exist i g 0 Show Transcribed Text ii g 9 c On which interval s is the graph increasing decreasing or constant

4 Write the equation for the line of best fit shown in the graph below Show all your work 3 points Distance in miles 765 432 Hiking Club Results e 9 0 0 1 2 3 4 5 6 7 8 Time in hours

Find the value of each variable 6 101 8 14

Find the numerical value of the area under the normal curve that is below z 0 99 O Area 0 8389 O Area 0 1611 O Area 0 0985 Area 0 7861

45 45 90 Special Right Triangle Multiplying Radicals 2 3 6 4 4 16 4 b 45 1 a 5 b 5 c 5 2 8 a 3 45 D C 43 C a 45 X b a 45 4 5 20 2158 6 6 30 7 b 7 2 45 C c 7 2 a 45 C b 45 b C 43 X 25 45 Leg X Hypotenuse 9 2 Dividing Radicals 2 15 3 a 6 b b 6 C 3 X 4 2 y 5 II 45 6 2 a a a C b 45 19 45 X 2 b X 45 VIO 16 a 8 b C b 10 3 45 Y 45 Note The legs of a 45 45 90 triangle are always congruent T y a 28 y C 45 J

What is the surface area of the square pyramid shown 5 inches A 100 inches B 105 inches C 125 inches D 185 inches 8 inches 5 inches

Select the correct answer Consider the given functions 2 1 0 1 2 3 f x 48 24 12 6 3 1 5 g x 2 5 Select the true statement regarding the end behavior of the functions OA As the value of x increases fand g both approach positive infinity OB As the value of x increases fis the only function to approach 0 OC As the value of x increases fand h both approach positive infinity OD As the value of x increases g is the only function to approach 0 h x N A

9 C 44 b Multiplying Radicals 2 3 6 2 30 Special Right Triangle 5 S 3 60 A As 60 60 2 3 C 30 32 X 10 ya 9 4 a b 8 i 6 30 x b 46 5 60 x 60 y a J Shorter Leg X Longer Leg X3 Hypotenuse 2x Adrian Dividing Radicals A A 60 a C 11 J 60 2 y 3 8 60 7 3 60 a 20 11 y 2 5 3 Note The shorter leg is always opposite the 30 angle and the longer leg is always opposite the 60 angle 2 1 2 60 O a b 9 3 30 83 U BO a 30 943 X y 60

11 A polynomial function g is graphed below 3 2 A 2 1 0 1 a Give a formula for g x with the smallest possible degree To find the leading coefficie use the fact that the point 2 1 is on the graph

346 257 12 1 8 832 50 x 7 What is the value of the bolded number 4 2 891 3 4 071 Round the following numbers to the thousands place 5 6 541 2 4 739 8 500 28 13 Solve the following problems 6 2 278 70 x 2 9 523 328 Solve the following problems 14 40 x 5 10 303 56 Finish the fact families 15 20 x 3 II 732 456 16 50 x4

To the nearest cubic centimeter what is the volume of the regular hexagonal prism www 3 The volume of the regular hexagonal prism is about cm Do not round until the final answer Then round to the nearest whole number as needed 6 cm 13 cm 5 2 cm

Lesson 13 Reasoning about Exponential Graphs Part 2 Cool Down Two Graphs Here are two graphs representing the function f given by f x 10 2 and the function g defined by g x a b y 2 48 0 3 g 1 12 X 1 Is b greater than or less than 2 Explain how you know 2 Write an equation that defines g Show your reasoning IL 3 f and g represent the number in thousands of social media followers of two organizations as a function of years since 2010 What does the intersection of f and g mean in this context

A glass bead has the shape of a rectangular prism with a smaller rectangular prism removed What is the volume of the glass that forms the bead The volume of the glass that forms the bead is S cm 3 6 cm Question Help 4 cm Jen 7 an 6 cm The figure is not to scale

Graph y x 2 10 9 8 7 6 5 4 3 2 1 10 2 4 D 3 3 5 6 9 6 5 4 2 1 8 7 2 3 S 6 8 9 IC

Find the area of A RST if r 45 cm S 53 cm include and t 80 cm Be sure to the units in your answer In AABC Find B 60 C 42 and b 90 ft the lengths of sides a and c

Find the ratio of BL to LF B E A F 2 14 C Given EFII BD BC CD Find the ratio of BL to LF

Which of the following choices corresponds to the graph O 6 5 4 3 2 1 0 1 2 3 4 5 6 O x x 4 ax 4 x x 4 O x x 4 PO

csc 27 3 16 csc tan 3 7 2 17 tan 18 cot 390