Sequences & Series Questions and Answers

Given g x is a transformation of the graph f x 2 determine which of the below correctly describe g x f x 2x 4324 4523 33 Amplote v 0 g x 2 x 4 g x 2x 4 g x 2 x 4 g x 2x 4 54 Asymptote

O 543 2 of which graph below does not have an inverse 5 4 3 2 1 4 2 31 543 2 1 5 A 3 2 12 31 2345 2 3 5 31 2 23 3 T V 1 2 3 T 9 3 4 18000 S 5 5

Consider the graphs of the functions f x and g x f x g x What is the value of f g 2 2 4 6 6 5

Which investment would be worth the most after 15 years O O An initial investment of 5000 compounded semi annually at a rate of 6 after 15 years An initial investment of 5000 compounded quarterly at a rate of 5 9 after 15 years An initial investment of 5000 compounded continuously at a rate of 5 8 after 15 years

1080 bacteria 120 bacteria 320 bacteria Question 5 14 3 points A person purchased a used Honda Civic for 6500 The car is expected to decrease in value by 12 each year over the next several years Which function model below best describes the value of the car tyears after it was purchased Op t 6500 1 12x Op t 6500 0 88 p t 6500 0 12 p t 6500 6500 12 x

the expression 2x4 2x 4 Evaluate using properties of exponent 27 1 3

by graphing the related function unction Choose the correct graph below Q O OB Ay

olve for x 4 x 6 17 3x Vrite the exact inswer usi

10 a 1 x 1 x D x 1 x 1 1 x 1 x 1 1 x 1 x 1 x 1 x 1 d x 1 x 1 x 1 1 x 1 Find the Taylor polynomial P4 for f x In x at xo 1 b c x 1 x 1 I

Which of the following series is conditionally convergent co O A OB 1 B 1 8 A 1 00 1 n 2n 3 n 1 4 1 sin C 1 00 In n n 1 0015 n 1 n 7 n n 2 D F1 E Both C and D

Problem The aquarium has 10 more red fish than blue fish 60 of the fish are red How many blue fish are in the aquarium

Part 2 of 2 Give the domain and range of the quadratic function whose graph is described The vertex is 6 8 and the parabola opens up The domain of fis 0 00 Type your answer in interval notation Type your answer in interval notation The range of the function is

Find the inverse function of f x 4x 5 The inverse function f x

Homing pigeons avoid flying over large bodies of water preferring to fly around them instead Assume that a pigeon released from a boat 5 miles from the shore of a lake point B in the figure flies first to point P on the shore and then along the straight edge of the lake to reach its home at L If L is 10 miles from point A the point on the shore closest to the boat and if a pigeon needs as much energy per mile to fly over water as over land find the location of point P which minimizes energy used 5 miles Point P is miles away from point A Type an exact answer using radicals as needed

Determine which three out of the six points shown below are a solution to the equation 3x y 6 Plot the three points that are in the solution set draw a line through the three points and then answer the questions below 5 9 1 9 4 6 3 3 6 6 7 3 Plot three points by clicking You can delete a point by clicking it 10 9 8 543 2 1 y 10 9 8 7 10 6 10 3 2 1 1 2 3 2 5 6 7 8 9 1 5 6 7 8 9 10

What is the error term in the approximation f x f x 2h 3 f x 4f x h 2 h

d e C 6 9 erle X 6 14 10 30 CHECK C Check x

2 Homework Solve the equation with rational expone x 6 3 2 27

Assume the consumption of electricity is increasing at 3 per year If it continues to increase at this rate indefinitely find the number of years befor the electric utilities will need to double their generating capacity The electric utilities will need to double their generating capacity in about Round to the nearest year as needed years

13 of 15 Determine the equation of the oblique asymptote of the function 2x 5x12 f x x 3 Oy x 11 Oy 2x 11 y 2x 1 O Oy x 1 N

x Clear Solve Undo 4 x 7 9 Redo

Holly Krech is planning for her retirement so she is setting up a payout annuity with her bank She wishes to receive a payout of 1 700 per month for twenty years Round your answers to the nearest cent a How large a monthly payment must Holly Krech make if she saves for her payout annuity with an ordinary annuity which she sets up thirty years before her retirement The two annuities pay the same interest rate of 7 8 compounded monthly b How large a monthly payment must she make if she sets the ordinary annuity up twenty years before her retirement

cts Restaurant Food Truck A restaurant has a main location and a traveling food truck The first matrix A shows the number of managers and associat The second matrix B shows the average annual cost of salary and benefits in thousands of dollars Complete parts a thr Managers Associates 4 A Salary Benefits 8 4 2 Question 14 6 5 51 BE Part 2 of 4 a Find the matrix product AB AB 720 128 245 44 24 7 Simplify your answer Managers Associates HW Score 79 17 14 25 points Points 1 25 of 5 CITE 42 23 1 8 B b Explain what AB represents Choose the correct answer below OA Row 1 of AB represents the restaurant and row 2 represents the food truck Column 1 of AB repre benefits in thousands and column 2 represents total salary in thousands for all employees OB Row 1 of AB represents the food truck and row 2 represents the restaurant Column 1 of AB repre salary in thousands and column 2 represents total benefits in thousands for all employees OC Row 1 of AB represents the food truck and row 2 represents the restaurant Column 1 of AB repre benefits in thousands and column 2 represents total salary in thousands for all employees OD Row 1 of AB represents the restaurant and row 2 represents the food truck Column 1 of AB repre salary in thousands and column 2 represents total benefits in thousands for all employees

Decide if the following series converge or diverge SPECIFY the TEST you are using then JUSTIFY your answer using that test 1 5 pts n 1 2 n nn TEST ANS

h expression has the smallest value ct one 3 3 5 D 3 3 4 E 3 3 6 3 3 5

A pole is 192 5 cm tall If 0 4 in equals one cm how many feet tall is the pole Select one O a 6 4 ft O b 77 ft O c 25 7 ft O d 48 ft

12 A 61 year old couple is considering opening a business of their own They will either purchase an established Gift and Card Shoppe or open a new Wine Boutique The Gift Shoppe has a continuous income stream with an annual rate of flow at time t given by G t 30 200 dollars per year The Wine Boutique has a continuous income stream with a projected annual rate of flow at time t given by W t 19 900e0 08t dollars per year The initial investment is the same for both businesses and money is worth 10 compounded continuously Find the present value of each business over the next 4 years until the couple reaches age 65 to see which is the better buy Round your answers to the nearest dollar

The distance formula may be written as Select one O a D XB XA YB YA D XB XA YB YA D XB XA YB YA OC O d D XB XA YB YA O b

Solve 4 tan x 4 0 x 2 Separate your answers with a comm X

c Continue adding terms in this series to complete the list below Carry each sum to at least 8 decimal places IM IM IM IM IM IMG IM IM IM IM k k k k k k 1 d The sums in the table in part c form k a sequence whose nth term is Sn 12 Based on your calculations in the table do you think the sequence S converges or diverges Explain How do you think this sequence S is related to the series 1 1 2

Wa Solution 11 A candy store is building a display with two base of each prism is a square with a edge le prism is 12 inches tall and the other is twice a are stacked so that the pieces do not overlap volume of the display A 36 cubic inches B 60 cubic inches 180 cubic inches

hether the following statement makes sense or does not make se 1 e exponents I simplified 201 correct answer below 1 20 and obtained 400 1 1 statement does not make sense I get 20 20 20 20 1 e statement does make sense I get 202 20 40 40 1600 1 e statement does not make sense I get 20 20 400 400 1 1 e statement does make sense I get 20 20 400 400

0314 Chapter 3 SkiII BUIK K Identify the polynomial 7y8 4y 5

A 3 Multiply x 7 x 7 x 7x 49 x 49 B x 7x 49 D x 49

1 3x 1 2x 5 6x 17 5 6x 17x 5 B 6x 17x 5 6x 17 5x

er 3 Mastery Quiz Determine whether the following statement makes sense or does not make sense and explain the reasoning 1 By adding the exponents I simplified 3 3 and obtained 9 Choose the correct answer below O C OD Question 1 of 37 The statement does make sense I get 1 1 get 3 3 5 5 9 3 3 9 9 9 The statement does not make sense I get 32 3 9 9 1 The statement does not make sense I get 32 32 3 3 The statement does make sense I get 3 3 6 6 36

75 7 cm 27 57 m Type an integer or a decimal

K Convert the given u 0 016 ml to de 0 016 ml 00 016 Type an integer o

Quiz Me 7 2 4 Select app olume termine the metric unit that would be

Find the value of the function from the graph when x 1 Y 3 2 0 0 1 5 3x 6y 9 2 3 0 03

If f x 3x 2x 1 then find f 0 0 1

6 Find the area of the surface that is formed by revolving each graph on the given about the given ax a y x 1 on the interval 1 5 about the x axis b y x on the interval 1 8 about the y axis

Choose the best answer to indi Choose the correct answer belo 7753 cm 7753 dm 3

Which expression is equivalent to 64y100 84 100 2 8y10 8y50 O 32y10 O 32 50

Find the radius of convergence R of the series R 00 I n 3 2 3n Find the interval I of convergence of the series Enter your answer using interval notati

2 You have seen that you can calculate values of the sine function using right triangles formed by a radius of the unit circle Values of that result in 30 60 90 or 45 45 90 triangles are used frequently on exercises and tests because their sine and cosine values can be found exactly without using a calculator You should learn to recognize these values quickly and easily The same is true for values of cose and sine that correspond to the x and y intercepts of the unit circle The central angles that correspond to these special values of x are 30 45 60 90 120 135 150 180 210 225 240 270 300 315 and 330 What these angles have in common is that they are all multiples of 30 or 45 and some of them are also multiples of 60 or 90 Copy and complete a table like the one below for all special angles between 0 and 360 Degrees Radians 0 0 30 I 45 60 90 120

State if each triangle is 13 74 in 5 in 7 in

Use Synthetic Division to evaluate 3x 2x 5x 1 when x G 202 23 218 247

3 Given that u 3 1 2 v 0 1 1 and w 1 1 2 are vectors in R Find a 2u 2w b wl C W

1 2 3 4 5 4 Compare Contrast each of the following Exponential Equations by filling in the table X y 100 0 90 y 100 0 90 2x a 2 25 6 64 19 58 57 76 b 400 80 16 3 2 x 5 For the given situation pattern determine the Exponential Function that describes it y a b x y 100 0 90 2 c A computer virus siphons a bank account by 1 2 per year The account last year had 12000000 d Every time a ball bounces it loses a third of its height To test this a scientist tosses a ball off a 50ft building and records the height for each bounce