Sequences & Series Questions and Answers

10 Factor to find all x intercepts of the function f x 2x 4x 8x 16

Solve the logarithmic equation log 20 x 5 1 log 20 X 6 Determine the equation to be solved after removing the logarithm x 5 x 6 20 Type an equation Do not simplify Select the correct choice below and if necessary fill in the answer box to com OA The solution set is Simplify your answer Type an exact answer Use a comma to separat B There is no solution

3x If f x In x g x e x and h x x find the following a fog x What is the domain of fog b gof x What is the domain of g of c fog 7 d foh x What is the domain of f o h e foh e a fog x Simplify your answer The domain of fog is b gof x Simplify your answer The domain of g of is Type your answer in interval notation c fog 7 Simplify your answer d f x Simplify your answer Type your answer in interval notation

The magnitude and direction of two forces acting on an object are 120 pounds S70 E and 60 pounds N68 E respectively Find the magnitude to the nearest hundredth of a pound and the direction angle to the nearest tenth of a degree of the resultant force

Using the graph of f shown below find three intervals on which f is one to one making each interval as large as possible Ay 3 6 Q G The intervals on which f is one to one are 1 00 Simplify your answers 8 4 1 and

16 Z 6 4 Z 5 2i I Find 2 22 in rectangular form I Find 2 22 in Polar form III Verify your answers from Part 1 Part I Tv Show 2 2 and 2 2 in an Argand Dia

How to solve x from the following equation 5x4 2x 300 0

4 Find the exact value of the following logarithmic expression log 81 1081

h solving the triangle Enter your answer as a decimal value A ZA LB LC 19 38 b degrees a b C C 14

Finish solving the triangle Enter your answer as a decimal value You must be accurate to at least 3 decimal places ZA LB 20 b 31 31 degrees a b C 14

9 Use the functions f x x 1 and g x 4x 4 tc answer the following m When f x 0 n When g x 0 p When f x g x

The temperature a of water in an ice cube tray is 75 F when it is placed in a freezer Its temperature n hours after being placed in the freezer is 20 less than 1 hour earlier a Find a formula for the nth term of the geometric sequence that gives the temperature of the water n hours after it is placed in the freezer an b Find the temperatures of the water 6 hours and 12 hours after it is placed in the freezer Round your answers to two decimal places a6 a12 F F c Use a graphing utility to graph the sequence to approximate the time required for the water to freeze Round your answer to one decimal place hr

12 Given the function f x x2 1 where n is a Natural number using calculus methods determine the intervals of concavity Show all work for full marks

Oil leaked from a tank at a rate of r t liters per hour The rate decreased as time passed and values of the rate at two hour time intervals are shown in the table t h 0 2 4 6 8 10 r t L h 8 9 7 5 6 9 6 2 5 7 5 3 Find lower and upper estimates for the total amount of oil in liters that leaked from the tank over the interval 0 10 Use five equal subintervals lower estimate upper estimate

dare Using a national random sample from the NEXT Generation Health Study researchers compared alcohol and drug impaired driving between high school seniors with those one year post high school The sample included 2407 high school seniors and 2178 subjects one year post high school All sub jects in the study completed a questionnaire that in cluded several questions related to recent alcohol and drug use with the following table reporting the inci dence of several of these behaviors for the two groups Binge drinking refers to at least four for females or five for males drinks within two hours 23 Explain why it is not correct to use a chi square test on this table to compare the high school seniors and post high school graduate groups Alcohol drinking at least once last 30 days Binge drinking at least once last 30 days Used marijuana at least once last year Used illicit drugs other than marijuana at least once last year High School Post High School Seniors Graduates 787 402 583 157 1044 583 654 162

A ngle B measures 17 and BC has length 10 find Angle C in degrees The length of AB 18 17

If AC has length 4 and BC has length 15 find The length of AB The measure of angle B in degrees The measure of angle C in degrees 4 A 15 B

Test Question 17 of 20 Find the sum of the first 9 terms of the geometric series 4 12 36 The sum of the first 9 terms of the geometric series is Simplify your answer

A ZA LB ZC b 43 33 C degrees C a b C 15 PO B

ng the triangle A C ZA ZB ZC 67 B b degrees degrees a a b C 9 7 C

A 20 ft ladder leans against a building so that the angle between the ground and the ladder is 72 degrees How high does the ladder reach on the building Your answer is feet

D redit 8 How high can you go using s 2 4 1 1 7 4 2 3 2 1 32 2741 24 2 2 3 7 4 3 4 4 5 7 4 2 5 6 4 2 6 7 7 8 4x2 8 D 9 7 2 9 10 11 7 4 11 12 7 2 17 14 2 12 13 7 4 2 11 2 13 14 7 4 2 28 2 14 15 2x4 7 8 7 15 16 42 16 7x2 4 14 4 10 17 24 7 17 18 72 4 18 19 41 7 2 24 7 17 2 19 20 4 21 22 41 2 24 2 22 23 27 4 23 24 7x4 2 28 2 24 25 7 4 49 24 25 26 41 2 24 2 26 27 27 28 7x4 28 72 49 74 2401 42 16 27 128 47 16384 2 4 4 14 2 47 74 42 42 312 29 24 42 27 72 7 5040 4 24 21 2 16384 128 2401 49 149 7

D redit 8 How high can you go using s 2 4 1 1 7 4 2 3 2 1 32 2741 24 2 2 3 7 4 3 4 4 5 7 4 2 5 6 4 2 6 7 7 8 4x2 8 D 9 7 2 9 10 11 7 4 11 12 7 2 17 14 2 12 13 7 4 2 11 2 13 14 7 4 2 28 2 14 15 2x4 7 8 7 15 16 42 16 7x2 4 14 4 10 17 24 7 17 18 72 4 18 19 41 7 2 24 7 17 2 19 20 4 21 22 41 2 24 2 22 23 27 4 23 24 7x4 2 28 2 24 25 7 4 49 24 25 26 41 2 24 2 26 27 27 28 7x4 28 72 49 74 2401 42 16 27 128 47 16384 2 4 4 14 2 47 74 42 42 312 29 24 42 27 72 7 5040 4 24 21 2 16384 128 2401 49 149 7

ided by the following curves Let S be the solid generated when R is revolved about the given axis If possible find the volume of S by both the disk washer and shell methods Check that your results agree y x y x OA S 1 11 in the first quadrant revolved about the x axis Set up the integral s that gives the volume of the solid as a single integral if possible using the disk washer method Use increasing limits of integration Select the correct choice below and fill in any answer boxes within your choice OB dx S dx Type exact answers www dx Type exact answers

Select the correct asnwer The volume of a rectangular prism is a minimum of 25 cubic feet The height of the prism is 3 feet more than its width and its length is at most 5 feet more than the width Carla wrote this system of inequalities to represent this situation where Vis the volume of the prism and wis the width V w 8w 15w V 25 A OB C OD Carla wrote the system incorrectly the first equation has the wrong volume expression Carla wrote the system incorrectly the second equation has the wrong inequality symbol Carla wrote the system correctly Carla wrote the system incorrectly the first equation has the wrong inequality symbol

Solve the equation Check your answer in the original example 4m 6 9 3

9 Given A ABC answer the following round each answer to the nearest tenth A If a 10 b 6 and c 7 find a 2 points find ZA b 2 points find ZB c 2 points find ZC 6 C 7 10 B

12 5 points Prove identity sin x csc x cos x csc x

Consider the following vectors given in polar form 3 3 70 Write the polar form for each of the following resultant vectors a 50 7 Preview 13 325 6 67 Preview Hint your answers will be in the form c and you do not need to enter a degree symbol Enter your angle as a degrees between 0 and 360

Find the standard deviation for the following data Round your answer to 2 decimal places as needed 90 63 53 96 26 4 52 73 13 10 19 standard deviation

Find the periodic payment which will amoun to a sum of 18000 if an interest rate 8 is compounded annually at the end of 14 consecutive years

A certain game involves tossing 3 fair coins and it pays 19 for 3 heads 10 for 2 heads and 4 for 1 head Is 10 a fair price to pay to play this game That is does the 10 cost t blay make the game fair

A theater has 24 rows of seats The first row has 18 seats the second row has 20 seats the third row has 22 seats and so on How many seats are in the theater The theater has seats

Find n when a 36 d 4 and an 24 n

Expand x 4 5 x 4 Simplify your answer

Find the 11th term of the arithmetic sequence 11 7 3 3 5 a11 Simplify your answer

10 Find each product 10 4a 3a 4 4a 3a 8 A 16a 9a 32 B 16a 24a 25a 12a 32 C 16a 7a 36a 32 D 16a 24a 25a 12a 32 State if the given binomial is a factor of the given polynomial 11 11 8x 57x 10x 15x 45x 21 x 7 A No B Yes 12 12 a 4 a 1 a A No B Yes

3 Find the exact value of the following logarithmic expression 1 F log11

The value of Tony s investment was 1140 on January 1st On this date three years later investment was worth 1824 The average rate of change for this investment was 19 p 4 year 1 day 2 month 3 quarter

5 no calculator what is the value of 4x 5 if x 3

2 Identify the value for x that is not a solution to the inequality 4 4x 8 a 0 b 2 c 3 d 10

3 Choose the value for x below that is not a solution to the inequality 3x 10 a 4 b 3 CO c 2 d 1 e 0

4 Find the point on the line x 3y 2 0 that is closest to the point 2 1 A Enter your answer symbolically enter your answe

y 2 x 1 x y 1 Ty 4 3 2 3 2 1 0 2 3 1 2 3 4 X 1

x y 6x 8y 21 0 6 9 4 6 5 4 3 2 1 1 0 1 2 3 1 1 2 3 5 6 X

Find the indicated term of the geometric sequence 2 6 18 54 the 7th term The 7th term of the geometric sequence is

Use a system of two equations in two variables a and d to write a formula for the general term the nth term of the arithmetic sequence whose seventh term a7 is 8 and whose ninth term ag is 18

Write a formula for the general term the nth term of the arithmetic sequence below Then use the formula for an to find a20 the 20th term of the sequence 4 10 16 22 The formula is an 6n 2 Simplify your answer

Find n when a 7 d 7 and an 35 n

Write a formula for the general term the nth term of the arithmetic sequence below Then use the formula for a to find a20 the 20th term of the 4 10 16 22 The formula is an 1 Simplify your answer www