Sequences & Series Questions and Answers

1 2x 3 x 4x 3 2 5 5 dx integralini hesaplay n z

13 20 points Determine if the function is 1 1 If the function is 1 1 find its inverse a f x x 4 9r 8 7 2 b f z x 9 f x c f x J 2 I d f x 3r 3 f x

Consider the right triangle shown below where a 6 79 612 7 and 14 4 Note that and are measured in radias a What is the value of cos p cos o cos 6 79 14 4 b What is the value of sin sin sin 12 7 14 4 c What is the value of tan o tan 4 an112 7 6 79 d What is the value of tan 1 1 8703 Preview COS Preview sin Preview tan Preview 6 79 14 4 12 7 14 4 12 7 6 79 0 8908753383550616 0 7719763260918318 3 237299169760396 Box 1 Enter your answer as a number like 5 3 2 2172 or as a calculation like 5 3 2 3 5 4 Enter DNE for Does Not Exist oo for Infinity

Find the sum of the first 5 terms of the following sequence 3 13 23 33

Interpreting a Linear Equation Lewis invested some money in an account The balance in the account is given by the equation B 8200 45t where t is the number of years since the initial investment was made and B is the account balance The equation tells us that Lewis started with S account is Select an answer at a rate of in the account and that the balance in the Select an answer

The balance sheet provides a snapshot of the financial condition of a company Investors and analysts use the information given on the bal and other financial statements to make several interpretations regarding the company s financial condition and performance Green Caterpillar Garden Supplies Inc is a hypothetical company Suppose it has the following balance sheet items reported at the end of it of operation For the second year some parts are still incomplete Use the information given to complete the balance sheet Green Caterpillar Garden Supplies Inc Balance Sheet for Year Ending December 31 Millions of Dollars Year 2 Year 1 Year 2 Year 1 Assets Current assets Cash and equivalents Accounts receivable Inventories Total current assets Net fixed assets Net plant and equipment Total assets 2 953 8 662 19 687 43 750 6 457 2 363 6 930 15 750 Liabilities and equity Current liabilities Accounts payable Accruals Notes payable Total current liabilities Long term debt 19 250 Total debt Common equity Common stock Retained earnings Total common equity 35 000 Total liabilities and equity 0 410 2 324 8 203 10 937 21 328 32 813 43 750 0 0 2 187 2 187 6 563 8 750 17 063 9 187 26 250 35 000

2 Rewrite using only positive exponents x 7 5 Make sure you preview your answer using the button and make sure the computer interprets your entry corrrectly Use parentheses for grouping if needed answer

6 The following graph is a representation of y 1 2 Using your graphing calculator or another graphing utility determine what the result of the graph would be as you change the 2 to different values including negative values and positive values less than 1 What happens when you change the 1 What happens if you change the a to a 2x or x On your assignments and exams you ll need to know how basic changes in exponential equations change the shape of the graph Come back to this question after completing this self check for some useful feedback y

3 Explain why the exponential growth and expor decay graphs curve the way they do for each si

Solve the inequality x 15x 44 0 x or x

7 Evaluate the expression 5x2y when and y 4 X 5x y

4 Evaluate the expression 5xy when x 2 and y 1 5xy 4

Find all solutions to the equation in the interval 0 2 Enter the solutions in increasing order sin 2x 2 sin x x 0 T Remember sin 20 2 sin 0 cos 0 Enter

Suppose that two students perform a titration experiment multiple times resulting in the average concentrations reported here Student A 0 125 0 008 M Student B 0 12 0 03 M The more precise work was done by Choose because Choose St Choose that student has fewer significant figures reported in their average that student found a higher average concentration that student s data has a larger standard deviation that student s data has a smaller standard deviation

Find the 8 th term a 8 for the sequence a n 5n 7

stress strain diagram obtained from a tensile test of a metallic material find out values for asked properties a Modulus of Elasticity b Yield Stress Strain at ftacture e Uniform Strain g Resillience MPa 300 250 200 150 100 8 0 5 1 6 2 c Ultimate Tensile Stress d 5 5 9x Ductility

Use a method based on contour integration to evaluate the sum 2n 1 00 11 1

572 230z 98y 0 1 1 1 1 1 The largest intervals that may be considered for the domain of the solution to 571 230ry 98 0 are either For oo type inf and for oo type inf 2 Let C and C be arbitrary constants The general solution to the homogeneous differential equation 572 230ry 980s the function C e C e C 0 3 The unique solution to the initial value problem for at 57z y 230ry 98y 0 1 1 s 1 1

10 Evaluate 4 x 4x 4x2x2x 2x 2 O 1024 O 1062 O 1024 OC 1062

15 Which system of equations is represented in the following graph y X

11 Find the coordinates of the ordered pair where the maximum value occurs P 8x 6y 43 given these constraints for the equation 4x 5y 25 2 15 y 13 O 15 7 O 10 13 O 5 9 5 1

14 Solve the system of equations by substitution y 3x 3 y 3x 21 X y

15 Which expression can be substituted for in the top equation of the system below to solve the system by substitution 3x 11y 7 2 7y 11 O11 7y 07 11y Olly 7

5 Solve the system of equations by elimination 13y 1 3x 13y 73 11x X y

3 On a separate piece of paper solve the system of equations by graphing and check each solution with the feedback after submission More than one answer may be correct check all that apply y x 4 4x 5y 10 0y 7 Oy 6 Ox 1 x 6 x 3 Oy 0 These two lines have no solutions These two lines have infinite solutions

7 State the number of solutions for the linear system of equations 2y 10x 14 5y 25x 75 O Infinite solutions O No solutions O One solution

Reflect the vector 3 7 across the x axis 2

A normal temperature for a certain animal is 73 7 F If a temperature x that differs from the normal by at leas 1 4 F is considered unhealthy write the condition for an unhealthy temperature x as an inequality involving an absolute value and solve for x

The number of accidents that occur each day at a certain intersection along with the corresponding probabilities are shown Accidents 0 1 Probability 935 03 2 02 3 01 4 005 Find the expected number of accidents each day

x 5 f x 8 A x 2 if 4 x 1 if x 1 if x 1 5 B Q Q O C Q O D d Based on the graph find the range Select the correct choice below and fill in the answer box es to complet your choice A The range has at least one isolated value It can be described as the union of the interval s set Type your answer in interval notation Use a comma to separate answers as needed OB The range consists exclusively of one or more isolated values It can be described as Use a comma to separate answers as needed OC The range does not have any isolated values It can be described by and the

Find the explicit definition of this sequence 7 14 21 28 an 7n 7 B an 7n C an 7n 1 7

Find the sixth term of the geometric sequence given the first term and common ratio a 100 and r 2

Find the domain of the given function x 10 3 X 5x F x The domain of F is Type your answer in interval notation

Find a formula for the nth term of the arithmetic sequence First term 10 Common difference 3 an n

Find the explicit definition of this sequence 11 23 35 47 an 11n 1 B an 2n 1 11 an 12n 1

How much would you have to deposit in an account with a 4 75 interest rate compounded continuously to have 20 000 in your account 20 years later P Round to the nearest cent

500 were deposited into an account with a 5 interest rate compounded monthly How many years was it in the bank if the current amount is 2469 t years Round to the nearest year

log729 log x 1 log728 terimleri aritmetik bir dizinin ard k 3 terimi oldu una g re x ka t r A 4 B 6 C 8 D 10 E 12

Identify the key features of the graph of f x 4 Select all that apply 1 0 8 6 2 10 co 8 6 4 2 2 4 6 CO 8 10 2 4 8 10 This image cannot be easily described If you need an explanation of this image please ask your teacher help As x approaches positive infinity f x approaches negative infinity O The function has an x intercept of 0 1 and no y intercepts As x approaches negative infinity f x approaches 0 which means that the function has an asymptote of y O The value of the function decreases throughout its domain O The value of the function increases throughout its domain The function has a y intercept of 0 1 and no x intercepts

Find the final amount of money in an account if 7 300 is deposited at 7 5 interest compounded quarterly every 3 months and the money is left for 9 years The final amount is 5 Round answer to 2 decimal places

The function p t 450 0 985 represents how a particular penguin population is declining eac year t How many years will it take for the penguin population to drop to just 100 0 226 years O 99 274 years O 0 756 years O 99 5 years

Write f x x 5 Z7 x as a multiplication of prime polynomials

log5 56x 1 O 16x 1 O 6x 1 O 256x 1 55 6x 1 Question 12 Simplify log1 5 6 75 log1 5 2 O log1 5 O log1 5 3 375 O log1 5 13 5 2 O log1 5 6 75 4 75

What would you type into a calculator to evaluate log3 50 log 3 log 50 O log 3 50 log 50 log 3 log 50 3

Unit 6 Lesson 10 Practice Problem 2 Modified Q P P 1 1 YA Match each point with its radian measure I I I 1 R J 1 1 1 1 R I N X Q

Use first and second differences to determine whether the sequence 2 6 8 34 50 is linear quadratic or neither Note the first term in the sequence corresponds to x 1 a The sequence is O linear quadratico neither b If the sequence is linear or quadratic write an equation for the sequence in terms of x If neither enter DNE The equation is y c If the sequence is linear or quadratic find the next term in the sequence If neither enter DNE The next term is

The annual number of homicides in a given city for a 10 year period is shown 99 107 121 114 Find the values of Q1 Q2 and Q3 Q1 Q2 Q3 92 X S 89 110 109 115 108

1 2 3 4 5 Consider the two data sets below Data set 1 Average monthly high temperature in Chicago Average monthly high temperature in Los Angeles Data set 2 Which data set would you expect to have the greater standard deviation You would expect data set Choose one to have the greater standard deviation 1 2

In one recent year the mean price of all new homes sold in the United States was 372 500 The median price on the other hand was 272 000 Which of the two measures of average do you think is a more accurate representation of what a typical homebuyer could expect to pay for a new home Why Choose the correct answer The mean because that s the most commonly used measure of average The median because that reflects the price right in the middle of the range and a relatively small number of super expensive homes won t affect it that much The median because the mean doesn t seem very realistic O The mean because it factors in ALL of the prices not just some O The median because everyone wants to pay less for a house O The mean because if they re expecting to pay more it ll be great to end up not paying as much

A club is holding a raffle Ten thousand tickets have been sold for 2 each There will be a 1st prize of 3000 3 second prizes of 1000 each 5 third prizes of 500 each and 20 consolation prizes of 100 each Find the expected winnings of a single ticket X P 2 9971 98 498 998 0020 0005 0003 2998 0001