Sequences & Series Questions and Answers

mathematical induction on integer n to prove each of the following statements 1 1 n 1 for m 2 3 4 5 3n n 1 6 n 1 1 3 2 3 1 3 3 4

Rewrite the logarithm as a ratio of common logarithms and natural loga log 20 a common logarithms b natural logarithms

Convert the following degree measur to radians 102 50 radians

II Let C denote the k 1 x k 1 matrix 0 where I denotes the vector of 1 s and A is a k x k symmetric matrix of ranl such that I A 0 Find C 1

graph 5 4 32 3 2 34 23 3 4 to answer the following questions A The graph represents a function yes no no B The domain is

et S represent the statement 10 20 40 5 25 21 2 and use mathematical induction to prove that S is true for every positive integer n Follow these steps a Verify S b Write S c Write S 1 d Assume that S is true and use algebra to change S to S e Write a conclusion based on Steps a to d

2 a For f x 3x 5 Calculate and simplify the difference quotient f x h f x

The following sketch represents the distance d in miles that Kevin was from home as a function of time t in hours Answer the questions based on the graph shown to the right In parts a to g how many hours elapsed and how far was Kevin from home during this time Complete parts a through i How far was Kevin from home during this time O 0 5 miles 8 miles between 0 to 8 miles Obetween 1 to 1 5 miles c From t 1 5 to t 2 how many hours elapsed hour s elapsed d t 1 8 1 5 8 2 9 7 3 3 1 7 3 2 0 2 2 0 4 3 0 t

The line for a Lineweaver Burk plot was determined to be y 0 01x 0 003 1 What are the Km and Vmax of the enzyme Round to the nearest hundredth for each don t include any units Km Vmax

f x x 2 16 x 2 3x 10 for x 5 and x 2 g x x 2 4 x 2 7x 12 for x 3 and x 4 What is f g x

Which transformation s can be used to show that polygon W 2 4 x 2 8 Y 6 2 Z 4 4 is similar to polygon L 3 0 M 3 8 N 13 4 O 9 0

f x 0 2x 0 7x 4x 5 on the interval 6 4 and approximate any local maxima and local minima b Determine where f is increasing and where it is decreasing a Using a graphing utility graph the function for 6 x 4 and 25 y 10 Choose the correct graph below OA OB Q The local maximum is y 1 20 and it occurs at x 1 67 Round to two decimal places The local minimum is y and it occurs at x k Q Q

1 point For each of the recursively defined sequences given below write out the next four terms of the sequence Hint Take note of the index of the first term a ai 1 3 c Ck b bj j b 1 with bo 3 1 8a 1 i with a 1 1 1 Ck 12ck 2 with co 1 and c 1 1 1 3 1 1 d dn ndn 1 dn 2 with d 1 and d 3 7 1

To select groups for a project a teacher asked her students to select a colored marble from a bag and Then whoever had the same colored marbles at the end of the drawing process were in the same gro Libby wanted to calculate the probability that they picked the same colored marble would they have t event as independent or dependent Explain your answer in a complete sentence You do not need calculate the probability

The function P y 0 034y2 3 642y 252 560 represents the population P in millions of people in 2005 that were y years of age or older a Identify the dependent and independent variable O The dependent variable is y and the independent variable is P The dependent variable is P and the independent variable is y

A carwash charges 8 per car and can wash at most 10 cars each hour The amount the carwash earns in an hour depends on the number of cars washed What is the domain of this relation A 0 x 10 OB 0 x 80 C 0 1 2 3 4 5 6 7 8 9 10

Six lights are arranged in a row Each light is also a button When a button is pressed its own light and all the lights neighboring it i e to the left an the right are toggled i e any light that was off is turned on and vice versa Figure out which buttons to press to tur all the lights if the starting position is as shown above For each button enter 1 if the button should be pressed and 0 if it should not be pressed

me mplete d the lateral and total surface area of each figure 4 cm 6 cm 4 cm 10 cm

Find the point that is symmetric to the point 4 5 with respect to the x axis the y axis and the origin The point symmetric to 4 5 with respect to the x axis is Type an ordered pair

y x x 4 y 45x 33 y 3x 1 300 y 50 z y 5 1 20 Linear O O O O Nonlinea O O O

Carl Dehne has 80 000 in an account paying 4 8 interest compounded monthly He plans to use up all the money by making equal monthly withdrawals for 15 years If the interest rate is 4 8 find the amount of each withdrawal

Consider the equation 5x y 3 A line parallel to the above line would have a slope of perpendicular to the above line would have a slope of A line

Two cyclists 72 miles apart start riding toward each other at the same time One cycles 3 times as fast as the other If they meet 3 hours later what is the speed in mi h of the faster cyclist a Write an equation using the information as it is given above that can be solved to answer this problem Use the variable r to represent the speed of the slower cyclist b What is the speed of the faster cyclist

Give the equation for each graph 5 4 3 2 1 SY Cha ww Bux XXX A ma 4 3 P 7 4 5 I

Solve for 1 2 7 x 8 5 40 I

Write the linear inequality for this graph 40 10 9 8 7 6 5 4 3 2 y Select an answer a 465 4 9 84 6 3 ft

Write the equation of the line passing through the points 7 0 and 7 3 Be sure to use exact values The equation is

For the function f x x 6x a f 1 8 b f 9 c f r 22 ir 3 3 evaluate

Problem 7 Assume that you guess that n 2 i 0 a2n b for constants a and b Use constructive induction to verify the formula and derive a a

Question 18 Submit Question Write the equation of the line passing through the points 7 0 and 7 3 Be sure to use exact values The equation is

Express Bi 2 in simplest a bi form

Solve the system by elimination 4x 3y 6y SERENDE O No solution 16 25 Infinite number of solutions

The table lists the average tuition and fees at private colleges and universities for selected years Year 1985 1990 1995 2000 2008 Tuition and Fees in dollars 5407 9299 12 412 16 192 a Find the equation of the least squares regression line that models the data 25 144 ya Type the slope as a decimal rounded to three decimal places Round the y intercept to the nearest int

The equation for line r can be written as y 4 x 2 Line s is perpendicular to liner and 9 passes through 3 5 What is the equation of line s

If 14500 dollars is invested at an interest rate of 5 percent per year find the value of the investment at the end of 5 years for the following compounding methods to the nearest cent a Annual b Semiannual c Monthly d Daily

d an an a n 1 d an an 1 0 Question 1 an 1 31 28 25 22 an art Cn 1 d an 31 n 1 3 an 31 3n 3 an 34 3n adding a 31 d 29 3 3

Solve the system by elimination 5x 5y 15 Multiply by 3 15x 15y 45 4x 3y 19 Multiply by 5 20x 15y 95 35x 140 5 4 5y 15 20 5y 15 5y 5 5 5 20 A 35 X 4 35

1 Write the arithmetic sequence 32 24 16 in the standard form find an

List the interval s on which f is increasing The interval s on which fis increasing is are Type your answer in interval notation Use a comma to separate answers as needed II AN

The graph of a function y f x can have more than one of which type of intercept Choose the correct answer below Oy intercept x intercept both an x intercept and a y intercept neither an x intercept nor a y intercept

Solve the equation 1 3 89 27 p p Type a whole number fraction

Instructions Find the common ratio of the geometric sequence Write your answer as a fraction Use a forward slash i e for all fractions e g 1 2 for 1 2 1 27 9 3 1 3 Common Ratio

Find the average rate of change of g x 5x 4 from x 4 to x 4 Next Question

4 3 2 H 5 4 3 2 1 2 3 4 1 2 3 4 5 The function graphed above is Increasing on the interval s Decreasing on the interval s

Find the domain of the function f x 3x 2 The domain is Type your answer in interval notation

Find the domain of the function g x X 2 X 4 The domain of the function is

3 2m m 0 2 to be connected with drivers who charge the passengers a fee for the ride Uber has set up an algorithm in the app that charges users different pick up fees and a different fee per mile based on how far the trip is Below is the layout of the different charges they apply Let c m represent the total charge of the trip based on the number of miles m driven a You and your friends want to get lunch from Jim s Pizza after school Jim s Pizza is approximately 1 5 miles away from the high school How much will Uber charge you for this ride Show your work 2 Points b Using c m complete the tables of values 2 Points c m 3 c m 5 1 50m 772 2 10 3 2m 5 1 50m 15 0 75m 20 0 25m c m 8 20 if 5 1 50m 2 Sandom 5 772 15 0 75m 0 m 2 2 m 10 10 m 20 m 20 10 20 c m 80 15 0 75 10 16 0 75 26 20 0 25m m 20 c m 25 20 0 26 20 3 4 c Would Uber charge you 25 00 or 30 00 for a ride to Hartford which is approximately 20 miles away from WHS Explain how you determined your answer 2 Points

16402 Let there be n N and positive numbers x x2 xn that verify the equation 1 1 n Show that x2 Xn n 1 1 X 2 1 r 6 1 r n n 1 n 2 n 1

A bacteria population starts at 100 on oll bs3 1 Explain why the expressions 1000 210 Trots moin du nobamoini evig vino noitamoin 10126 00 therd ha Tuoy 107 gnidyns and 1000 2To both represent the h 2 mentisquoy grille enote8 8 bacteria population after h hours 2 By what factor door the bact maldong eri esvios 1 ab1 to 132 wan 6 101 191besluoy NEA Jhow Toy were nantis way raw zaloy y 1911A A nounslops is of so 69 nibs vivos srittesqen bre

23 Find the average rate of change of f x 2x from 4 to 0